LMFDB - Embedded newform 147.7.f.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,7,Mod(19,147)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("147.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	147.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$33.8179502921$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.3
Root			$-2.30325 + 3.98935i$ of defining polynomial
Character	$\chi$	$=$	147.19
Dual form			147.7.f.a.31.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80325 - 3.12332i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(25.4966 + 44.1614i) q^{4} +(-71.9311 - 41.5295i) q^{5} +56.2198i q^{6} +414.723 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(1.80325 - 3.12332i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(25.4966 + 44.1614i) q^{4} +(-71.9311 - 41.5295i) q^{5} +56.2198i q^{6} +414.723 q^{8} +(121.500 - 210.444i) q^{9} +(-259.420 + 149.776i) q^{10} +(221.304 + 383.310i) q^{11} +(-688.408 - 397.452i) q^{12} +696.494i q^{13} +1294.76 q^{15} +(-883.932 + 1531.01i) q^{16} +(5447.24 - 3144.96i) q^{17} +(-438.190 - 758.967i) q^{18} +(2327.56 + 1343.82i) q^{19} -4235.44i q^{20} +1596.27 q^{22} +(-7885.31 + 13657.8i) q^{23} +(-5598.76 + 3232.44i) q^{24} +(-4363.11 - 7557.12i) q^{25} +(2175.37 + 1255.95i) q^{26} +3788.00i q^{27} -23274.5 q^{29} +(2334.78 - 4043.95i) q^{30} +(-41177.0 + 23773.6i) q^{31} +(16459.0 + 28507.9i) q^{32} +(-5975.21 - 3449.79i) q^{33} -22684.6i q^{34} +12391.3 q^{36} +(5079.89 - 8798.64i) q^{37} +(8394.35 - 4846.48i) q^{38} +(-5428.63 - 9402.67i) q^{39} +(-29831.5 - 17223.2i) q^{40} +38165.4i q^{41} -151197. q^{43} +(-11285.0 + 19546.2i) q^{44} +(-17479.3 + 10091.7i) q^{45} +(28438.4 + 49256.7i) q^{46} +(43543.1 + 25139.6i) q^{47} -27558.3i q^{48} -31471.1 q^{50} +(-49025.1 + 84914.0i) q^{51} +(-30758.1 + 17758.2i) q^{52} +(99778.2 + 172821. i) q^{53} +(11831.1 + 6830.70i) q^{54} -36762.6i q^{55} -41896.1 q^{57} +(-41969.8 + 72693.8i) q^{58} +(-335347. + 193612. i) q^{59} +(33012.0 + 57178.4i) q^{60} +(10203.5 + 5890.98i) q^{61} +171479. i q^{62} +5575.73 q^{64} +(28925.0 - 50099.6i) q^{65} +(-21549.6 + 12441.7i) q^{66} +(192138. + 332792. i) q^{67} +(277772. + 160372. i) q^{68} -245840. i q^{69} +156126. q^{71} +(50388.8 - 87276.0i) q^{72} +(-325227. + 187770. i) q^{73} +(-18320.6 - 31732.3i) q^{74} +(117804. + 68014.1i) q^{75} +137051. i q^{76} -39156.7 q^{78} +(-16591.8 + 28737.9i) q^{79} +(127164. - 73418.4i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(119203. + 68821.8i) q^{82} -984986. i q^{83} -522434. q^{85} +(-272646. + 472237. i) q^{86} +(314206. - 181407. i) q^{87} +(91779.9 + 158967. i) q^{88} +(227430. + 131307. i) q^{89} +72791.1i q^{90} -804193. q^{92} +(370593. - 641886. i) q^{93} +(157038. - 90666.0i) q^{94} +(-111616. - 193325. i) q^{95} +(-444394. - 256571. i) q^{96} +575147. i q^{97} +107554. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} + 42 q^{5} - 454 q^{8} + 972 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 + 42 * q^5 - 454 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} + 42 q^{5} - 454 q^{8} + 972 q^{9} - 261 q^{10} - 1070 q^{11} + 4671 q^{12} - 756 q^{15} + 3911 q^{16} - 7212 q^{17} + 1215 q^{18} + 24606 q^{19} - 78 q^{22} - 15224 q^{23} + 6129 q^{24} + 22274 q^{25} + 19044 q^{26} + 32524 q^{29} + 2349 q^{30} - 40200 q^{31} + 70203 q^{32} + 28890 q^{33} - 84078 q^{36} - 45670 q^{37} - 503310 q^{38} + 93366 q^{39} + 94941 q^{40} - 445660 q^{43} - 188829 q^{44} + 10206 q^{45} + 525804 q^{46} - 82884 q^{47} - 1218884 q^{50} + 64908 q^{51} - 722856 q^{52} - 13034 q^{53} - 32805 q^{54} - 442908 q^{57} - 159501 q^{58} - 1810362 q^{59} + 429705 q^{60} + 392856 q^{61} - 1410446 q^{64} - 389004 q^{65} + 1053 q^{66} + 384094 q^{67} + 1616346 q^{68} + 225688 q^{71} - 55161 q^{72} - 903078 q^{73} + 1185530 q^{74} - 601398 q^{75} - 342792 q^{78} - 559592 q^{79} - 847713 q^{80} - 236196 q^{81} - 347634 q^{82} + 1953576 q^{85} - 2302402 q^{86} - 439074 q^{87} + 304887 q^{88} + 1770036 q^{89} - 113064 q^{92} + 361800 q^{93} + 1837620 q^{94} + 1160112 q^{95} - 1895481 q^{96} - 520020 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 + 42 * q^5 - 454 * q^8 + 972 * q^9 - 261 * q^10 - 1070 * q^11 + 4671 * q^12 - 756 * q^15 + 3911 * q^16 - 7212 * q^17 + 1215 * q^18 + 24606 * q^19 - 78 * q^22 - 15224 * q^23 + 6129 * q^24 + 22274 * q^25 + 19044 * q^26 + 32524 * q^29 + 2349 * q^30 - 40200 * q^31 + 70203 * q^32 + 28890 * q^33 - 84078 * q^36 - 45670 * q^37 - 503310 * q^38 + 93366 * q^39 + 94941 * q^40 - 445660 * q^43 - 188829 * q^44 + 10206 * q^45 + 525804 * q^46 - 82884 * q^47 - 1218884 * q^50 + 64908 * q^51 - 722856 * q^52 - 13034 * q^53 - 32805 * q^54 - 442908 * q^57 - 159501 * q^58 - 1810362 * q^59 + 429705 * q^60 + 392856 * q^61 - 1410446 * q^64 - 389004 * q^65 + 1053 * q^66 + 384094 * q^67 + 1616346 * q^68 + 225688 * q^71 - 55161 * q^72 - 903078 * q^73 + 1185530 * q^74 - 601398 * q^75 - 342792 * q^78 - 559592 * q^79 - 847713 * q^80 - 236196 * q^81 - 347634 * q^82 + 1953576 * q^85 - 2302402 * q^86 - 439074 * q^87 + 304887 * q^88 + 1770036 * q^89 - 113064 * q^92 + 361800 * q^93 + 1837620 * q^94 + 1160112 * q^95 - 1895481 * q^96 - 520020 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.80325	−	3.12332i	0.225406	−	0.390415i	−0.731035	−	0.682340i	$-0.760962\pi$
$2$	1.80325	−	3.12332i	0.225406	−	0.390415i	0.956441	+	0.291925i	$0.0942957\pi$
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$4$	25.4966	+	44.1614i	0.398384	+	0.690021i
$5$	−71.9311	−	41.5295i	−0.575449	−	0.332236i	0.183874	−	0.982950i	$-0.441136\pi$
$5$	−71.9311	−	41.5295i	−0.575449	−	0.332236i	−0.759323	+	0.650714i	$0.774470\pi$
$6$			56.2198i			0.260277i
$7$		0			0
$7$		0			0
$8$	414.723			0.810006
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$	−259.420	+	149.776i	−0.259420	+	0.149776i
$11$	221.304	+	383.310i	0.166269	+	0.287986i	0.937105	−	0.349047i	$-0.113495\pi$
$11$	221.304	+	383.310i	0.166269	+	0.287986i	−0.770836	+	0.637033i	$0.780161\pi$
$12$	−688.408	−	397.452i	−0.398384	−	0.230007i
$13$			696.494i			0.317020i	0.987357	+	0.158510i	$0.0506691\pi$
$13$			696.494i			0.317020i	−0.987357	+	0.158510i	$0.949331\pi$
$14$		0			0
$15$	1294.76			0.383633
$16$	−883.932	+	1531.01i	−0.215804	+	0.373783i
$17$	5447.24	−	3144.96i	1.10874	−	0.640131i	0.170237	−	0.985403i	$-0.445547\pi$
$17$	5447.24	−	3144.96i	1.10874	−	0.640131i	0.938503	+	0.345272i	$0.112213\pi$
$18$	−438.190	−	758.967i	−0.0751354	−	0.130138i
$19$	2327.56	+	1343.82i	0.339344	+	0.195920i	0.659982	−	0.751281i	$-0.270564\pi$
$19$	2327.56	+	1343.82i	0.339344	+	0.195920i	−0.320638	+	0.947202i	$0.603897\pi$
$20$		−	4235.44i		−	0.529430i
$21$		0			0
$22$	1596.27			0.149912
$23$	−7885.31	+	13657.8i	−0.648090	+	1.12252i	0.335489	+	0.942044i	$0.391098\pi$
$23$	−7885.31	+	13657.8i	−0.648090	+	1.12252i	−0.983579	+	0.180480i	$0.942235\pi$
$24$	−5598.76	+	3232.44i	−0.405003	+	0.233828i
$25$	−4363.11	−	7557.12i	−0.279239	−	0.483656i
$26$	2175.37	+	1255.95i	0.123770	+	0.0714584i
$27$			3788.00i			0.192450i
$28$		0			0
$29$	−23274.5			−0.954304			−0.477152	−	0.878821i	$-0.658331\pi$
$29$	−23274.5			−0.954304			−0.477152	+	0.878821i	$0.658331\pi$
$30$	2334.78	−	4043.95i	0.0864732	−	0.149776i
$31$	−41177.0	+	23773.6i	−1.38220	+	0.798012i	−0.992419	−	0.122897i	$-0.960782\pi$
$31$	−41177.0	+	23773.6i	−1.38220	+	0.798012i	−0.389778	+	0.920909i	$0.627448\pi$
$32$	16459.0	+	28507.9i	0.502290	+	0.869991i
$33$	−5975.21	−	3449.79i	−0.166269	−	0.0959955i
$34$		−	22684.6i		−	0.577158i
$35$		0			0
$36$	12391.3			0.265589
$37$	5079.89	−	8798.64i	0.100288	−	0.173704i	−0.811515	−	0.584331i	$-0.801357\pi$
$37$	5079.89	−	8798.64i	0.100288	−	0.173704i	0.911803	+	0.410627i	$0.134690\pi$
$38$	8394.35	−	4846.48i	0.152981	−	0.0883234i
$39$	−5428.63	−	9402.67i	−0.0915159	−	0.158510i
$40$	−29831.5	−	17223.2i	−0.466117	−	0.269113i
$41$			38165.4i			0.553756i	0.960905	+	0.276878i	$0.0892998\pi$
$41$			38165.4i			0.553756i	−0.960905	+	0.276878i	$0.910700\pi$
$42$		0			0
$43$	−151197.			−1.90168			−0.950841	−	0.309679i	$-0.899779\pi$
$43$	−151197.			−1.90168			−0.950841	+	0.309679i	$0.899779\pi$
$44$	−11285.0	+	19546.2i	−0.132478	+	0.229458i
$45$	−17479.3	+	10091.7i	−0.191816	+	0.110745i
$46$	28438.4	+	49256.7i	0.292167	+	0.506048i
$47$	43543.1	+	25139.6i	0.419397	+	0.242139i	0.694819	−	0.719184i	$-0.255484\pi$
$47$	43543.1	+	25139.6i	0.419397	+	0.242139i	−0.275422	+	0.961323i	$0.588818\pi$
$48$		−	27558.3i		−	0.249189i
$49$		0			0
$50$	−31471.1			−0.251769
$51$	−49025.1	+	84914.0i	−0.369580	+	0.640131i
$52$	−30758.1	+	17758.2i	−0.218751	+	0.126296i
$53$	99778.2	+	172821.i	0.670206	+	1.16083i	0.977846	+	0.209328i	$0.0671275\pi$
$53$	99778.2	+	172821.i	0.670206	+	1.16083i	−0.307640	+	0.951503i	$0.599539\pi$
$54$	11831.1	+	6830.70i	0.0751354	+	0.0433795i
$55$		−	36762.6i		−	0.220962i
$56$		0			0
$57$	−41896.1			−0.226229
$58$	−41969.8	+	72693.8i	−0.215106	+	0.372575i
$59$	−335347.	+	193612.i	−1.63282	+	0.942708i	−0.649600	+	0.760277i	$0.725063\pi$
$59$	−335347.	+	193612.i	−1.63282	+	0.942708i	−0.983219	+	0.182431i	$0.941603\pi$
$60$	33012.0	+	57178.4i	0.152833	+	0.264715i
$61$	10203.5	+	5890.98i	0.0449530	+	0.0259536i	0.522308	−	0.852757i	$-0.325071\pi$
$61$	10203.5	+	5890.98i	0.0449530	+	0.0259536i	−0.477355	+	0.878711i	$0.658404\pi$
$62$			171479.i			0.719508i
$63$		0			0
$64$	5575.73			0.0212697
$65$	28925.0	−	50099.6i	0.105325	−	0.182429i
$66$	−21549.6	+	12441.7i	−0.0749562	+	0.0432760i
$67$	192138.	+	332792.i	0.638834	+	1.10649i	0.985689	+	0.168575i	$0.0539165\pi$
$67$	192138.	+	332792.i	0.638834	+	1.10649i	−0.346854	+	0.937919i	$0.612750\pi$
$68$	277772.	+	160372.i	0.883408	+	0.510036i
$69$		−	245840.i		−	0.748350i
$70$		0			0
$71$	156126.			0.436213			0.218107	−	0.975925i	$-0.430012\pi$
$71$	156126.			0.436213			0.218107	+	0.975925i	$0.430012\pi$
$72$	50388.8	−	87276.0i	0.135001	−	0.233828i
$73$	−325227.	+	187770.i	−0.836022	+	0.482677i	−0.855910	−	0.517125i	$-0.827002\pi$
$73$	−325227.	+	187770.i	−0.836022	+	0.482677i	0.0198883	+	0.999802i	$0.493669\pi$
$74$	−18320.6	−	31732.3i	−0.0452111	−	0.0783080i
$75$	117804.	+	68014.1i	0.279239	+	0.161219i
$76$			137051.i			0.312206i
$77$		0			0
$78$	−39156.7			−0.0825130
$79$	−16591.8	+	28737.9i	−0.0336521	+	0.0582872i	−0.882361	−	0.470573i	$-0.844047\pi$
$79$	−16591.8	+	28737.9i	−0.0336521	+	0.0582872i	0.848709	+	0.528860i	$0.177380\pi$
$80$	127164.	−	73418.4i	0.248368	−	0.143395i
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$	119203.	+	68821.8i	0.216195	+	0.124820i
$83$		−	984986.i		−	1.72264i	−0.508059	−	0.861322i	$-0.669637\pi$
$83$		−	984986.i		−	1.72264i	0.508059	−	0.861322i	$-0.330363\pi$
$84$		0			0
$85$	−522434.			−0.850697
$86$	−272646.	+	472237.i	−0.428651	+	0.742446i
$87$	314206.	−	181407.i	0.477152	−	0.275484i
$88$	91779.9	+	158967.i	0.134679	+	0.233271i
$89$	227430.	+	131307.i	0.322609	+	0.186259i	0.652555	−	0.757741i	$-0.273697\pi$
$89$	227430.	+	131307.i	0.322609	+	0.186259i	−0.329946	+	0.944000i	$0.607030\pi$
$90$			72791.1i			0.0998507i
$91$		0			0
$92$	−804193.			−1.03275
$93$	370593.	−	641886.i	0.460732	−	0.798012i
$94$	157038.	−	90666.0i	0.189070	−	0.109159i
$95$	−111616.	−	193325.i	−0.130184	−	0.225484i
$96$	−444394.	−	256571.i	−0.502290	−	0.289997i
$97$			575147.i			0.630179i	0.949062	+	0.315089i	$0.102034\pi$
$97$			575147.i			0.630179i	−0.949062	+	0.315089i	$0.897966\pi$
$98$		0			0
$99$	107554.			0.110846
$100$	222489.	−	385362.i	0.222489	−	0.385362i
$101$	−634688.	+	366437.i	−0.616022	+	0.355661i	−0.775319	−	0.631570i	$-0.782411\pi$
$101$	−634688.	+	366437.i	−0.616022	+	0.355661i	0.159297	+	0.987231i	$0.449077\pi$
$102$	176809.	+	306242.i	0.166611	+	0.288579i
$103$	−908207.	−	524353.i	−0.831138	−	0.479858i	0.0231042	−	0.999733i	$-0.492645\pi$
$103$	−908207.	−	524353.i	−0.831138	−	0.479858i	−0.854242	+	0.519875i	$0.825978\pi$
$104$			288852.i			0.256788i
$105$		0			0
$106$	719700.			0.604274
$107$	−587412.	+	1.01743e6i	−0.479503	+	0.830524i	−0.999724	−	0.0235083i	$-0.992516\pi$
$107$	−587412.	+	1.01743e6i	−0.479503	+	0.830524i	0.520221	+	0.854032i	$0.325850\pi$
$108$	−167283.	+	96580.9i	−0.132795	+	0.0766690i
$109$	−367045.	−	635741.i	−0.283426	−	0.490908i	0.688800	−	0.724951i	$-0.258138\pi$
$109$	−367045.	−	635741.i	−0.283426	−	0.490908i	−0.972226	+	0.234043i	$0.924804\pi$
$110$	−114821.	−	66292.1i	−0.0862669	−	0.0498062i
$111$			158375.i			0.115803i
$112$		0			0
$113$	2.04925e6			1.42023			0.710116	−	0.704085i	$-0.248643\pi$
$113$	2.04925e6			1.42023			0.710116	+	0.704085i	$0.248643\pi$
$114$	−75549.2	+	130855.i	−0.0509935	+	0.0883234i
$115$	1.13440e6	−	654945.i	0.745885	−	0.430637i
$116$	−593421.	−	1.02783e6i	−0.380180	−	0.658490i
$117$	146573.	+	84624.0i	0.0915159	+	0.0528367i
$118$			1.39653e6i			0.849969i
$119$		0			0
$120$	536967.			0.310745
$121$	787829.	−	1.36456e6i	0.444709	−	0.770259i
$122$	36798.9	−	21245.8i	0.0202654	−	0.0117002i
$123$	−297470.	−	515233.i	−0.159856	−	0.276878i
$124$	−2.09975e6	−	1.21229e6i	−1.10129	−	0.635830i
$125$			2.02259e6i			1.03556i
$126$		0			0
$127$	−1.64688e6			−0.803991			−0.401995	−	0.915642i	$-0.631683\pi$
$127$	−1.64688e6			−0.803991			−0.401995	+	0.915642i	$0.631683\pi$
$128$	−1.04332e6	+	1.80709e6i	−0.497495	+	0.861687i
$129$	2.04116e6	−	1.17846e6i	0.950841	−	0.548968i
$130$	−104318.	−	180684.i	−0.0474821	−	0.0822413i
$131$	1.78472e6	+	1.03041e6i	0.793882	+	0.458348i	0.841327	−	0.540526i	$-0.181775\pi$
$131$	1.78472e6	+	1.03041e6i	0.793882	+	0.458348i	−0.0474457	+	0.998874i	$0.515108\pi$
$132$		−	351831.i		−	0.152972i
$133$		0			0
$134$	1.38589e6			0.575989
$135$	157313.	−	272475.i	0.0639388	−	0.110745i
$136$	2.25909e6	−	1.30429e6i	0.898085	−	0.518510i
$137$	−1.61460e6	−	2.79657e6i	−0.627919	−	1.08759i	−0.987969	−	0.154654i	$-0.950574\pi$
$137$	−1.61460e6	−	2.79657e6i	−0.627919	−	1.08759i	0.360050	−	0.932933i	$-0.382760\pi$
$138$	−767836.	−	443310.i	−0.292167	−	0.168683i
$139$		−	4.06719e6i		−	1.51443i	−0.653163	−	0.757217i	$-0.726558\pi$
$139$		−	4.06719e6i		−	1.51443i	0.653163	−	0.757217i	$-0.273442\pi$
$140$		0			0
$141$	−783776.			−0.279598
$142$	281533.	−	487630.i	0.0983252	−	0.170304i
$143$	−266973.	+	154137.i	−0.0912976	+	0.0527107i
$144$	214795.	+	372037.i	0.0719346	+	0.124594i
$145$	1.67416e6	+	966578.i	0.549153	+	0.317054i
$146$			1.35438e6i			0.435194i
$147$		0			0
$148$	518080.			0.159813
$149$	1.39737e6	−	2.42031e6i	0.422427	−	0.731666i	−0.573749	−	0.819031i	$-0.694511\pi$
$149$	1.39737e6	−	2.42031e6i	0.422427	−	0.731666i	0.996176	+	0.0873655i	$0.0278448\pi$
$150$	424860.	−	245293.i	0.125884	−	0.0726794i
$151$	−301549.	−	522299.i	−0.0875846	−	0.151701i	0.818905	−	0.573929i	$-0.194581\pi$
$151$	−301549.	−	522299.i	−0.0875846	−	0.151701i	−0.906490	+	0.422228i	$0.861248\pi$
$152$	965293.	+	557312.i	0.274871	+	0.158697i
$153$		−	1.52845e6i		−	0.426754i
$154$		0			0
$155$	3.94921e6			1.06051
$156$	276823.	−	479472.i	0.0729170	−	0.126296i
$157$	1.23763e6	−	714546.i	0.319810	−	0.184642i	−0.331498	−	0.943456i	$-0.607554\pi$
$157$	1.23763e6	−	714546.i	0.319810	−	0.184642i	0.651308	+	0.758814i	$0.274221\pi$
$158$	59838.4	+	103643.i	0.0151708	+	0.0262766i
$159$	−2.69401e6	−	1.55539e6i	−0.670206	−	0.386943i
$160$		−	2.73414e6i		−	0.667514i
$161$		0			0
$162$	−212960.			−0.0500903
$163$	2.78644e6	−	4.82625e6i	0.643408	−	1.11442i	−0.341259	−	0.939969i	$-0.610853\pi$
$163$	2.78644e6	−	4.82625e6i	0.643408	−	1.11442i	0.984667	−	0.174446i	$-0.0558135\pi$
$164$	−1.68544e6	+	973087.i	−0.382103	+	0.220607i
$165$	286536.	+	496295.i	0.0637862	+	0.110481i
$166$	−3.07643e6	−	1.77618e6i	−0.672546	−	0.388295i
$167$			2.24388e6i			0.481781i	0.970552	+	0.240890i	$0.0774394\pi$
$167$			2.24388e6i			0.481781i	−0.970552	+	0.240890i	$0.922561\pi$
$168$		0			0
$169$	4.34171e6			0.899498
$170$	−942080.	+	1.63173e6i	−0.191752	+	0.332125i
$171$	565597.	−	326548.i	0.113115	−	0.0653068i
$172$	−3.85501e6	−	6.67707e6i	−0.757600	−	1.31220i
$173$	5.95864e6	+	3.44022e6i	1.15082	+	0.664428i	0.949088	−	0.315012i	$-0.102008\pi$
$173$	5.95864e6	+	3.44022e6i	1.15082	+	0.664428i	0.201736	+	0.979440i	$0.435342\pi$
$174$		−	1.30849e6i		−	0.248383i
$175$		0			0
$176$	−782471.			−0.143526
$177$	3.01812e6	−	5.22754e6i	0.544273	−	0.942708i
$178$	820225.	−	473557.i	0.145436	−	0.0839677i
$179$	3.94643e6	+	6.83543e6i	0.688091	+	1.19181i	0.972455	+	0.233092i	$0.0748843\pi$
$179$	3.94643e6	+	6.83543e6i	0.688091	+	1.19181i	−0.284364	+	0.958716i	$0.591782\pi$
$180$	−891323.	−	514606.i	−0.152833	−	0.0882383i
$181$			2.63639e6i			0.444604i	0.974978	+	0.222302i	$0.0713571\pi$
$181$			2.63639e6i			0.444604i	−0.974978	+	0.222302i	$0.928643\pi$
$182$		0			0
$183$	−183663.			−0.0299687
$184$	−3.27022e6	+	5.66418e6i	−0.524956	+	0.909251i
$185$	−730805.	+	421931.i	−0.115421	+	0.0666386i
$186$	−1.33654e6	−	2.31496e6i	−0.207704	−	0.359754i
$187$	2.41099e6	+	1.39199e6i	0.368698	+	0.212868i
$188$			2.56390e6i			0.385858i
$189$		0			0
$190$	−805087.			−0.117377
$191$	−6.17120e6	+	1.06888e7i	−0.885665	+	1.53402i	−0.0407156	+	0.999171i	$0.512964\pi$
$191$	−6.17120e6	+	1.06888e7i	−0.885665	+	1.53402i	−0.844949	+	0.534846i	$0.820370\pi$
$192$	−75272.3	+	43458.5i	−0.0106349	+	0.00614004i
$193$	6.69614e6	+	1.15981e7i	0.931435	+	1.61329i	0.780871	+	0.624692i	$0.214776\pi$
$193$	6.69614e6	+	1.15981e7i	0.931435	+	1.61329i	0.150564	+	0.988600i	$0.451891\pi$
$194$	1.79637e6	+	1.03713e6i	0.246031	+	0.142046i
$195$			901793.i			0.121619i
$196$		0			0
$197$	−9.42468e6			−1.23273			−0.616365	−	0.787460i	$-0.711396\pi$
$197$	−9.42468e6			−1.23273			−0.616365	+	0.787460i	$0.711396\pi$
$198$	193946.	−	335925.i	0.0249854	−	0.0432760i
$199$	−4.91639e6	+	2.83848e6i	−0.623860	+	0.360186i	−0.778370	−	0.627805i	$-0.783953\pi$
$199$	−4.91639e6	+	2.83848e6i	−0.623860	+	0.360186i	0.154510	+	0.987991i	$0.450620\pi$
$200$	−1.80948e6	−	3.13411e6i	−0.226185	−	0.391764i
$201$	−5.18772e6	−	2.99513e6i	−0.638834	−	0.368831i
$202$			2.64311e6i			0.320672i
$203$		0			0
$204$	−4.99989e6			−0.588939
$205$	1.58499e6	−	2.74528e6i	0.183977	−	0.318658i
$206$	−3.27545e6	+	1.89108e6i	−0.374687	+	0.216326i
$207$	1.91613e6	+	3.31883e6i	0.216030	+	0.374175i
$208$	−1.06634e6	−	615653.i	−0.118497	−	0.0684142i
$209$			1.18957e6i			0.130302i
$210$		0			0
$211$	1.05196e6			0.111983			0.0559914	−	0.998431i	$-0.482168\pi$
$211$	1.05196e6			0.111983			0.0559914	+	0.998431i	$0.482168\pi$
$212$	−5.08801e6	+	8.81269e6i	−0.533999	+	0.924913i
$213$	−2.10770e6	+	1.21688e6i	−0.218107	+	0.125924i
$214$	2.11850e6	+	3.66935e6i	0.216166	+	0.374410i
$215$	1.08758e7	+	6.27913e6i	1.09432	+	0.631807i
$216$			1.57097e6i			0.155886i
$217$		0			0
$218$	−2.64750e6			−0.255544
$219$	2.92704e6	−	5.06978e6i	0.278674	−	0.482677i
$220$	1.62348e6	−	937319.i	0.152469	−	0.0880277i
$221$	2.19045e6	+	3.79397e6i	0.202935	+	0.351493i
$222$	494657.	+	285591.i	0.0452111	+	0.0261027i
$223$		−	9.96615e6i		−	0.898696i	−0.893357	−	0.449348i	$-0.851656\pi$
$223$		−	9.96615e6i		−	0.898696i	0.893357	−	0.449348i	$-0.148344\pi$
$224$		0			0
$225$	−2.12047e6			−0.186159
$226$	3.69531e6	−	6.40046e6i	0.320129	−	0.554480i
$227$	−1.59963e7	+	9.23545e6i	−1.36754	+	0.789552i	−0.990614	−	0.136690i	$-0.956354\pi$
$227$	−1.59963e7	+	9.23545e6i	−1.36754	+	0.789552i	−0.376930	+	0.926242i	$0.623020\pi$
$228$	−1.06821e6	−	1.85019e6i	−0.0901262	−	0.156103i
$229$	−1.17915e7	−	6.80784e6i	−0.981892	−	0.566896i	−0.0790512	−	0.996871i	$-0.525189\pi$
$229$	−1.17915e7	−	6.80784e6i	−0.981892	−	0.566896i	−0.902841	+	0.429975i	$0.858522\pi$
$230$		−	4.72412e6i		−	0.388273i
$231$		0			0
$232$	−9.65248e6			−0.772992
$233$	−5103.02	+	8838.68i	−0.000403422	+	0.000698747i	−0.866227	−	0.499651i	$-0.833462\pi$
$233$	−5103.02	+	8838.68i	−0.000403422	+	0.000698747i	0.865824	+	0.500349i	$0.166795\pi$
$234$	528616.	−	305196.i	0.0412565	−	0.0238195i
$235$	−2.08807e6	−	3.61664e6i	−0.160895	−	0.278678i
$236$	−1.71004e7	−	9.87291e6i	−1.30098	−	0.751120i
$237$		−	517281.i		−	0.0388581i
$238$		0			0
$239$	2.49567e6			0.182807			0.0914037	−	0.995814i	$-0.470865\pi$
$239$	2.49567e6			0.182807			0.0914037	+	0.995814i	$0.470865\pi$
$240$	−1.14448e6	+	1.98230e6i	−0.0827894	+	0.143395i
$241$	4.73752e6	−	2.73521e6i	0.338454	−	0.195407i	−0.321134	−	0.947034i	$-0.604064\pi$
$241$	4.73752e6	−	2.73521e6i	0.338454	−	0.195407i	0.659588	+	0.751627i	$0.270731\pi$
$242$	−2.84131e6	−	4.92129e6i	−0.200480	−	0.347242i
$243$	797162.	+	460241.i	0.0555556	+	0.0320750i
$244$			600800.i			0.0413581i
$245$		0			0
$246$	−2.14565e6			−0.144130
$247$	−935961.	+	1.62113e6i	−0.0621108	+	0.107579i
$248$	−1.70771e7	+	9.85944e6i	−1.11959	+	0.646394i
$249$	7.67720e6	+	1.32973e7i	0.497285	+	0.861322i
$250$	6.31718e6	+	3.64723e6i	0.404300	+	0.233423i
$251$			2.18424e6i			0.138127i	0.997612	+	0.0690637i	$0.0220012\pi$
$251$			2.18424e6i			0.138127i	−0.997612	+	0.0690637i	$0.977999\pi$
$252$		0			0
$253$	−6.98020e6			−0.431029
$254$	−2.96974e6	+	5.14374e6i	−0.181225	+	0.313890i
$255$	7.05286e6	−	4.07197e6i	0.425349	−	0.245575i
$256$	3.94117e6	+	6.82631e6i	0.234912	+	0.406880i
$257$	2.72638e7	+	1.57408e7i	1.60615	+	0.927313i	0.990220	+	0.139514i	$0.0445540\pi$
$257$	2.72638e7	+	1.57408e7i	1.60615	+	0.927313i	0.615933	+	0.787799i	$0.288779\pi$
$258$		−	8.50027e6i		−	0.494964i
$259$		0			0
$260$	2.94996e6			0.167840
$261$	−2.82785e6	+	4.89799e6i	−0.159051	+	0.275484i
$262$	6.43659e6	−	3.71616e6i	0.357892	−	0.206629i
$263$	−3.28881e6	−	5.69639e6i	−0.180789	−	0.313136i	0.761360	−	0.648329i	$-0.224532\pi$
$263$	−3.28881e6	−	5.69639e6i	−0.180789	−	0.313136i	−0.942149	+	0.335193i	$0.891198\pi$
$264$	−2.47806e6	−	1.43071e6i	−0.134679	−	0.0777569i
$265$		−	1.65749e7i		−	0.890665i
$266$		0			0
$267$	−4.09373e6			−0.215073
$268$	−9.79771e6	+	1.69701e7i	−0.509003	+	0.881619i
$269$	−190420.	+	109939.i	−0.00978263	+	0.00564801i	−0.504883	−	0.863188i	$-0.668464\pi$
$269$	−190420.	+	109939.i	−0.00978263	+	0.00564801i	0.495101	+	0.868836i	$0.335131\pi$
$270$	−567351.	−	982680.i	−0.0288244	−	0.0499253i
$271$	2.41082e7	+	1.39189e7i	1.21132	+	0.699354i	0.963046	−	0.269337i	$-0.0868045\pi$
$271$	2.41082e7	+	1.39189e7i	1.21132	+	0.699354i	0.248270	+	0.968691i	$0.420138\pi$
$272$			1.11197e7i			0.552570i
$273$		0			0
$274$	−1.16461e7			−0.566147
$275$	1.93115e6	−	3.34485e6i	0.0928576	−	0.160834i
$276$	1.08566e7	−	6.26807e6i	0.516377	−	0.298130i
$277$	2.87725e6	+	4.98354e6i	0.135375	+	0.234476i	0.925741	−	0.378159i	$-0.123443\pi$
$277$	2.87725e6	+	4.98354e6i	0.135375	+	0.234476i	−0.790366	+	0.612635i	$0.790109\pi$
$278$	−1.27032e7	−	7.33417e6i	−0.591258	−	0.341363i
$279$			1.15540e7i			0.532008i
$280$		0			0
$281$	1.75833e7			0.792467			0.396233	−	0.918150i	$-0.370317\pi$
$281$	1.75833e7			0.792467			0.396233	+	0.918150i	$0.370317\pi$
$282$	−1.41334e6	+	2.44798e6i	−0.0630232	+	0.109159i
$283$	−1.27466e7	+	7.35922e6i	−0.562385	+	0.324693i	−0.754102	−	0.656757i	$-0.771928\pi$
$283$	−1.27466e7	+	7.35922e6i	−0.562385	+	0.324693i	0.191717	+	0.981450i	$0.438594\pi$
$284$	3.98067e6	+	6.89472e6i	0.173780	+	0.300997i
$285$	3.01363e6	+	1.73992e6i	0.130184	+	0.0751615i
$286$			1.11179e6i			0.0475253i
$287$		0			0
$288$	7.99909e6			0.334860
$289$	7.71280e6	−	1.33590e7i	0.319535	−	0.553451i
$290$	6.03787e6	−	3.48597e6i	0.247565	−	0.142932i
$291$	−4.48283e6	−	7.76448e6i	−0.181917	−	0.315089i
$292$	−1.65843e7	−	9.57497e6i	−0.666115	−	0.384582i
$293$		−	3.49743e6i		−	0.139042i	−0.997580	−	0.0695210i	$-0.977853\pi$
$293$		−	3.49743e6i		−	0.139042i	0.997580	−	0.0695210i	$-0.0221471\pi$
$294$		0			0
$295$	3.21625e7			1.25280
$296$	2.10675e6	−	3.64900e6i	0.0812339	−	0.140701i
$297$	−1.45198e6	+	838299.i	−0.0554230	+	0.0319985i
$298$	−5.03961e6	−	8.72886e6i	−0.190436	−	0.329844i
$299$	−9.51254e6	−	5.49207e6i	−0.355863	−	0.205458i
$300$			6.93651e6i			0.256908i
$301$		0			0
$302$	−2.17508e6			−0.0789685
$303$	5.71219e6	−	9.89381e6i	0.205341	−	0.355661i
$304$	−4.11481e6	+	2.37569e6i	−0.146463	+	0.0845607i
$305$	−489299.	−	847490.i	−0.0172455	−	0.0298700i
$306$	−4.77385e6	−	2.75618e6i	−0.166611	−	0.0961930i
$307$			3.99694e7i			1.38138i	0.723152	+	0.690689i	$0.242692\pi$
$307$			3.99694e7i			1.38138i	−0.723152	+	0.690689i	$0.757308\pi$
$308$		0			0
$309$	1.63477e7			0.554092
$310$	7.12142e6	−	1.23347e7i	0.239046	−	0.414040i
$311$	2.88815e7	−	1.66747e7i	0.960148	−	0.554342i	0.0639296	−	0.997954i	$-0.479637\pi$
$311$	2.88815e7	−	1.66747e7i	0.960148	−	0.554342i	0.896219	+	0.443613i	$0.146303\pi$
$312$	−2.25138e6	−	3.89950e6i	−0.0741284	−	0.128394i
$313$	−1.62725e7	−	9.39495e6i	−0.530667	−	0.306381i	0.210621	−	0.977568i	$-0.432451\pi$
$313$	−1.62725e7	−	9.39495e6i	−0.530667	−	0.306381i	−0.741288	+	0.671187i	$0.765785\pi$
$314$		−	5.15402e6i		−	0.166478i
$315$		0			0
$316$	−1.69214e6			−0.0536259
$317$	1.01986e7	−	1.76645e7i	0.320156	−	0.554527i	−0.660364	−	0.750946i	$-0.729598\pi$
$317$	1.01986e7	−	1.76645e7i	0.320156	−	0.554527i	0.980520	+	0.196419i	$0.0629312\pi$
$318$	−9.71596e6	+	5.60951e6i	−0.302137	+	0.174439i
$319$	−5.15075e6	−	8.92136e6i	−0.158671	−	0.274827i
$320$	−401068.	−	231557.i	−0.0122396	−	0.00706656i
$321$		−	1.83137e7i		−	0.553682i
$322$		0			0
$323$	1.69050e7			0.501659
$324$	1.50555e6	−	2.60768e6i	0.0442649	−	0.0766690i
$325$	5.26349e6	−	3.03888e6i	0.153329	−	0.0885244i
$326$	−1.00493e7	−	1.74059e7i	−0.290056	−	0.502393i
$327$	9.91021e6	+	5.72167e6i	0.283426	+	0.163636i
$328$			1.58281e7i			0.448545i
$329$		0			0
$330$	2.06678e6			0.0575113
$331$	1.06774e7	−	1.84939e7i	0.294431	−	0.509969i	−0.680422	−	0.732821i	$-0.738203\pi$
$331$	1.06774e7	−	1.84939e7i	0.294431	−	0.509969i	0.974852	+	0.222852i	$0.0715366\pi$
$332$	4.34983e7	−	2.51138e7i	1.18866	−	0.686274i
$333$	−1.23441e6	−	2.13807e6i	−0.0334294	−	0.0579014i
$334$	7.00834e6	+	4.04627e6i	0.188094	+	0.108596i
$335$		−	3.19175e7i		−	0.848974i
$336$		0			0
$337$	−1.98824e7			−0.519493			−0.259746	−	0.965677i	$-0.583639\pi$
$337$	−1.98824e7			−0.519493			−0.259746	+	0.965677i	$0.583639\pi$
$338$	7.82918e6	−	1.35605e7i	0.202753	−	0.351178i
$339$	−2.76649e7	+	1.59723e7i	−0.710116	+	0.409986i
$340$	−1.33203e7	−	2.30714e7i	−0.338904	−	0.586999i
$341$	−1.82253e7	−	1.05224e7i	−0.459633	−	0.265369i
$342$		−	2.35539e6i		−	0.0588823i
$343$		0			0
$344$	−6.27049e7			−1.54037
$345$	−1.02096e7	+	1.76835e7i	−0.248628	+	0.430637i
$346$	2.14898e7	−	1.24072e7i	0.518806	−	0.299533i
$347$	1.66198e7	+	2.87863e7i	0.397774	+	0.688965i	0.993451	−	0.114259i	$-0.0364495\pi$
$347$	1.66198e7	+	2.87863e7i	0.397774	+	0.688965i	−0.595677	+	0.803224i	$0.703116\pi$
$348$	1.60224e7	+	9.25051e6i	0.380180	+	0.219497i
$349$		−	2.57850e7i		−	0.606584i	−0.952898	−	0.303292i	$-0.901914\pi$
$349$		−	2.57850e7i		−	0.606584i	0.952898	−	0.303292i	$-0.0980858\pi$
$350$		0			0
$351$	−2.63832e6			−0.0610106
$352$	−7.28490e6	+	1.26178e7i	−0.167030	+	0.289305i
$353$	4.82036e7	−	2.78303e7i	1.09586	−	0.632695i	0.160729	−	0.986999i	$-0.448615\pi$
$353$	4.82036e7	−	2.78303e7i	1.09586	−	0.632695i	0.935130	+	0.354304i	$0.115282\pi$
$354$	−1.08848e7	−	1.88531e7i	−0.245365	−	0.424985i
$355$	−1.12303e7	−	6.48381e6i	−0.251019	−	0.144926i
$356$			1.33915e7i			0.296810i
$357$		0			0
$358$	2.84656e7			0.620400
$359$	8.08714e6	−	1.40073e7i	0.174788	−	0.302742i	−0.765300	−	0.643674i	$-0.777409\pi$
$359$	8.08714e6	−	1.40073e7i	0.174788	−	0.302742i	0.940088	+	0.340932i	$0.110743\pi$
$360$	−7.24905e6	+	4.18524e6i	−0.155372	+	0.0897043i
$361$	−1.99112e7	−	3.44873e7i	−0.423230	−	0.733056i
$362$	8.23428e6	+	4.75406e6i	0.173580	+	0.100217i
$363$			2.45621e7i			0.513506i
$364$		0			0
$365$	3.11919e7			0.641451
$366$	−331190.	+	573637.i	−0.00675513	+	0.0117002i
$367$	−9.72318e6	+	5.61368e6i	−0.196703	+	0.113566i	−0.595117	−	0.803639i	$-0.702894\pi$
$367$	−9.72318e6	+	5.61368e6i	−0.196703	+	0.113566i	0.398414	+	0.917206i	$0.369561\pi$
$368$	−1.39401e7	−	2.41450e7i	−0.279720	−	0.484490i
$369$	8.03169e6	+	4.63710e6i	0.159856	+	0.0922926i
$370$			3.04339e6i			0.0600830i
$371$		0			0
$372$	3.77954e7			0.734194
$373$	−1.99988e7	+	3.46389e7i	−0.385369	+	0.667479i	−0.991820	−	0.127642i	$-0.959259\pi$
$373$	−1.99988e7	+	3.46389e7i	−0.385369	+	0.667479i	0.606451	+	0.795121i	$0.292593\pi$
$374$	8.69524e6	−	5.02020e6i	0.166214	−	0.0959635i
$375$	−1.57645e7	−	2.73049e7i	−0.298942	−	0.517782i
$376$	1.80583e7	+	1.04260e7i	0.339714	+	0.196134i
$377$		−	1.62106e7i		−	0.302534i
$378$		0			0
$379$	2.92098e7			0.536551			0.268276	−	0.963342i	$-0.413546\pi$
$379$	2.92098e7			0.536551			0.268276	+	0.963342i	$0.413546\pi$
$380$	5.69166e6	−	9.85824e6i	0.103726	−	0.179659i
$381$	2.22329e7	−	1.28362e7i	0.401995	−	0.232092i
$382$	2.22564e7	+	3.85493e7i	0.399269	+	0.691554i
$383$	−3.97181e7	−	2.29312e7i	−0.706955	−	0.408161i	0.102978	−	0.994684i	$-0.467163\pi$
$383$	−3.97181e7	−	2.29312e7i	−0.706955	−	0.408161i	−0.809933	+	0.586523i	$0.800496\pi$
$384$		−	3.25276e7i		−	0.574458i
$385$		0			0
$386$	4.82993e7			0.839805
$387$	−1.83704e7	+	3.18185e7i	−0.316947	+	0.548968i
$388$	−2.53993e7	+	1.46643e7i	−0.434837	+	0.251053i
$389$	−7.72431e6	−	1.33789e7i	−0.131223	−	0.227285i	0.792925	−	0.609319i	$-0.208557\pi$
$389$	−7.72431e6	−	1.33789e7i	−0.131223	−	0.227285i	−0.924148	+	0.382034i	$0.875224\pi$
$390$	2.81659e6	+	1.62616e6i	0.0474821	+	0.0274138i
$391$			9.91960e7i			1.65945i
$392$		0			0
$393$	−3.21249e7			−0.529254
$394$	−1.69951e7	+	2.94363e7i	−0.277865	+	0.481277i
$395$	2.38693e6	−	1.37810e6i	0.0387302	−	0.0223609i
$396$	2.74225e6	+	4.74972e6i	0.0441593	+	0.0764861i
$397$	−2.54737e7	−	1.47073e7i	−0.407118	−	0.235050i	0.282433	−	0.959287i	$-0.408859\pi$
$397$	−2.54737e7	−	1.47073e7i	−0.407118	−	0.235050i	−0.689551	+	0.724237i	$0.742192\pi$
$398$			2.04740e7i			0.324753i
$399$		0			0
$400$	1.54268e7			0.241043
$401$	5.70055e7	−	9.87364e7i	0.884064	−	1.53124i	0.0372810	−	0.999305i	$-0.488130\pi$
$401$	5.70055e7	−	9.87364e7i	0.884064	−	1.53124i	0.846783	−	0.531939i	$-0.178536\pi$
$402$	−1.87095e7	+	1.08019e7i	−0.287995	+	0.166274i
$403$	−1.65581e7	−	2.86796e7i	−0.252986	−	0.438185i
$404$	−3.23648e7	−	1.86858e7i	−0.490827	−	0.283379i
$405$			4.90455e6i			0.0738302i
$406$		0			0
$407$	4.49681e6			0.0666992
$408$	−2.03318e7	+	3.52158e7i	−0.299362	+	0.518510i
$409$	−2.99288e7	+	1.72794e7i	−0.437442	+	0.252557i	−0.702512	−	0.711672i	$-0.747938\pi$
$409$	−2.99288e7	+	1.72794e7i	−0.437442	+	0.252557i	0.265070	+	0.964229i	$0.414605\pi$
$410$	−5.71626e6	−	9.90086e6i	−0.0829393	−	0.143655i
$411$	4.35942e7	+	2.51691e7i	0.627919	+	0.362529i
$412$		−	5.34769e7i		−	0.764671i
$413$		0			0
$414$	1.38210e7			0.194778
$415$	−4.09059e7	+	7.08511e7i	−0.572324	+	0.991294i
$416$	−1.98556e7	+	1.14636e7i	−0.275805	+	0.159236i
$417$	3.17006e7	+	5.49071e7i	0.437180	+	0.757217i
$418$	3.71541e6	+	2.14509e6i	0.0508719	+	0.0293709i
$419$		−	3.73902e7i		−	0.508294i	−0.967166	−	0.254147i	$-0.918205\pi$
$419$		−	3.73902e7i		−	0.508294i	0.967166	−	0.254147i	$-0.0817948\pi$
$420$		0			0
$421$	−5.93910e7			−0.795929			−0.397965	−	0.917401i	$-0.630283\pi$
$421$	−5.93910e7			−0.795929			−0.397965	+	0.917401i	$0.630283\pi$
$422$	1.89694e6	−	3.28560e6i	0.0252416	−	0.0437198i
$423$	1.05810e7	−	6.10893e6i	0.139799	−	0.0807131i
$424$	4.13803e7	+	7.16728e7i	0.542870	+	0.940279i
$425$	−4.75338e7	−	2.74436e7i	−0.619206	−	0.357499i
$426$			8.77734e6i			0.113536i
$427$		0			0
$428$	−5.99080e7			−0.764105
$429$	2.40276e6	−	4.16170e6i	0.0304325	−	0.0527107i
$430$	3.92235e7	−	2.26457e7i	0.493334	−	0.284826i
$431$	2.97697e7	+	5.15627e7i	0.371829	+	0.644026i	0.989847	−	0.142137i	$-0.0453975\pi$
$431$	2.97697e7	+	5.15627e7i	0.371829	+	0.644026i	−0.618018	+	0.786164i	$0.712064\pi$
$432$	−5.79948e6	−	3.34833e6i	−0.0719346	−	0.0415314i
$433$		−	6.40730e7i		−	0.789244i	−0.918843	−	0.394622i	$-0.870876\pi$
$433$		−	6.40730e7i		−	0.789244i	0.918843	−	0.394622i	$-0.129124\pi$
$434$		0			0
$435$	−3.01349e7			−0.366102
$436$	1.87168e7	−	3.24184e7i	0.225825	−	0.391140i
$437$	−3.67071e7	+	2.11928e7i	−0.439851	+	0.253948i
$438$	−1.05564e7	−	1.82842e7i	−0.125630	−	0.217597i
$439$	1.31778e8	+	7.60819e7i	1.55757	+	0.899265i	0.997488	+	0.0708286i	$0.0225643\pi$
$439$	1.31778e8	+	7.60819e7i	1.55757	+	0.899265i	0.560084	+	0.828436i	$0.310769\pi$
$440$		−	1.52463e7i		−	0.178980i
$441$		0			0
$442$	1.57997e7			0.182971
$443$	−1.72920e7	+	2.99506e7i	−0.198899	+	0.344504i	−0.948172	−	0.317758i	$-0.897070\pi$
$443$	−1.72920e7	+	2.99506e7i	−0.198899	+	0.344504i	0.749273	+	0.662262i	$0.230403\pi$
$444$	−6.99408e6	+	4.03803e6i	−0.0799064	+	0.0461340i
$445$	−1.09062e7	−	1.88901e7i	−0.123763	−	0.214365i
$446$	−3.11275e7	−	1.79715e7i	−0.350864	−	0.202572i
$447$			4.35656e7i			0.487777i
$448$		0			0
$449$	−1.33795e8			−1.47809			−0.739047	−	0.673654i	$-0.764724\pi$
$449$	−1.33795e8			−1.47809			−0.739047	+	0.673654i	$0.764724\pi$
$450$	−3.82374e6	+	6.62291e6i	−0.0419615	+	0.0726794i
$451$	−1.46292e7	+	8.44616e6i	−0.159474	+	0.0920724i
$452$	5.22488e7	+	9.04976e7i	0.565798	+	0.979990i
$453$	8.14183e6	+	4.70069e6i	0.0875846	+	0.0505670i
$454$			6.66153e7i			0.711880i
$455$		0			0
$456$	−1.73753e7			−0.183247
$457$	−7.62638e6	+	1.32093e7i	−0.0799043	+	0.138398i	−0.903208	−	0.429202i	$-0.858795\pi$
$457$	−7.62638e6	+	1.32093e7i	−0.0799043	+	0.138398i	0.823304	+	0.567600i	$0.192128\pi$
$458$	−4.25262e7	+	2.45525e7i	−0.442649	+	0.255564i
$459$	1.19131e7	+	2.06341e7i	0.123193	+	0.213377i
$460$	5.78465e7	+	3.33977e7i	0.594298	+	0.343118i
$461$		−	3.05013e7i		−	0.311326i	−0.987810	−	0.155663i	$-0.950249\pi$
$461$		−	3.05013e7i		−	0.311326i	0.987810	−	0.155663i	$-0.0497514\pi$
$462$		0			0
$463$	−1.61661e8			−1.62878			−0.814388	−	0.580320i	$-0.802927\pi$
$463$	−1.61661e8			−1.62878			−0.814388	+	0.580320i	$0.802927\pi$
$464$	2.05731e7	−	3.56336e7i	0.205942	−	0.356703i
$465$	−5.33144e7	+	3.07811e7i	−0.530256	+	0.306143i
$466$	18404.0	+	31876.7i	0.000181868	+	0.000315004i
$467$	−5.70833e7	−	3.29570e7i	−0.560478	−	0.323592i	0.192860	−	0.981226i	$-0.438224\pi$
$467$	−5.70833e7	−	3.29570e7i	−0.560478	−	0.323592i	−0.753337	+	0.657635i	$0.771557\pi$
$468$			8.63049e6i			0.0841972i
$469$		0			0
$470$	−1.50612e7			−0.145067
$471$	−1.11387e7	+	1.92927e7i	−0.106603	+	0.184642i
$472$	−1.39076e8	+	8.02955e7i	−1.32259	+	0.763599i
$473$	−3.34605e7	−	5.79553e7i	−0.316191	−	0.547659i
$474$	−1.61564e6	−	932788.i	−0.0151708	−	0.00875886i
$475$		−	2.34529e7i		−	0.218834i
$476$		0			0
$477$	4.84922e7			0.446804
$478$	4.50032e6	−	7.79479e6i	0.0412060	−	0.0713708i
$479$	7.96535e7	−	4.59880e7i	0.724767	−	0.418444i	−0.0917379	−	0.995783i	$-0.529242\pi$
$479$	7.96535e7	−	4.59880e7i	0.724767	−	0.418444i	0.816505	+	0.577339i	$0.195909\pi$
$480$	2.13105e7	+	3.69109e7i	0.192695	+	0.333757i
$481$	6.12820e6	+	3.53812e6i	0.0550678	+	0.0317934i
$482$		−	1.97291e7i		−	0.176183i
$483$		0			0
$484$	8.03478e7			0.708660
$485$	2.38855e7	−	4.13710e7i	0.209368	−	0.362636i
$486$	2.87496e6	−	1.65986e6i	0.0250451	−	0.0144598i
$487$	9.53763e7	+	1.65197e8i	0.825759	+	1.43026i	0.901338	+	0.433117i	$0.142586\pi$
$487$	9.53763e7	+	1.65197e8i	0.825759	+	1.43026i	−0.0755785	+	0.997140i	$0.524080\pi$
$488$	4.23162e6	+	2.44313e6i	0.0364122	+	0.0210226i
$489$			8.68725e7i			0.742944i
$490$		0			0
$491$	8.85504e7			0.748077			0.374038	−	0.927413i	$-0.377973\pi$
$491$	8.85504e7			0.748077			0.374038	+	0.927413i	$0.377973\pi$
$492$	1.51689e7	−	2.62734e7i	0.127368	−	0.220607i
$493$	−1.26782e8	+	7.31975e7i	−1.05807	+	0.610880i
$494$	3.37554e6	+	5.84661e6i	0.0280003	+	0.0484980i
$495$	−7.73647e6	−	4.46665e6i	−0.0637862	−	0.0368270i
$496$		−	8.40569e7i		−	0.688856i
$497$		0			0
$498$	5.53757e7			0.448364
$499$	2.61754e7	−	4.53371e7i	0.210665	−	0.364882i	−0.741258	−	0.671220i	$-0.765770\pi$
$499$	2.61754e7	−	4.53371e7i	0.210665	−	0.364882i	0.951923	+	0.306338i	$0.0991038\pi$
$500$	−8.93202e7	+	5.15690e7i	−0.714561	+	0.412552i
$501$	−1.74893e7	−	3.02923e7i	−0.139078	−	0.240890i
$502$	6.82210e6	+	3.93874e6i	0.0539271	+	0.0311348i
$503$		−	1.34114e8i		−	1.05383i	−0.849919	−	0.526914i	$-0.823349\pi$
$503$		−	1.34114e8i		−	1.05383i	0.849919	−	0.526914i	$-0.176651\pi$
$504$		0			0
$505$	6.08718e7			0.472653
$506$	−1.25871e7	+	2.18014e7i	−0.0971566	+	0.168280i
$507$	−5.86130e7	+	3.38402e7i	−0.449749	+	0.259663i
$508$	−4.19898e7	−	7.27285e7i	−0.320297	−	0.554771i
$509$	1.62222e8	+	9.36588e7i	1.23014	+	0.710224i	0.967060	−	0.254549i	$-0.0819269\pi$
$509$	1.62222e8	+	9.36588e7i	1.23014	+	0.710224i	0.263084	+	0.964773i	$0.415260\pi$
$510$		−	2.93711e7i		−	0.221417i
$511$		0			0
$512$	−1.05118e8			−0.783188
$513$	−5.09038e6	+	8.81679e6i	−0.0377049	+	0.0653068i
$514$	9.83269e7	−	5.67690e7i	0.724074	−	0.418044i
$515$	4.35522e7	+	7.54347e7i	0.318852	+	0.552267i
$516$	1.04085e8	+	6.00936e7i	0.757600	+	0.437401i
$517$			2.22540e7i			0.161041i
$518$		0			0
$519$	−1.07255e8			−0.767216
$520$	1.19959e7	−	2.07774e7i	0.0853142	−	0.147769i
$521$	3.89027e7	−	2.24605e7i	0.275085	−	0.158820i	−0.356111	−	0.934444i	$-0.615898\pi$
$521$	3.89027e7	−	2.24605e7i	0.275085	−	0.158820i	0.631196	+	0.775623i	$0.282564\pi$
$522$	1.01987e7	+	1.76646e7i	0.0717021	+	0.124192i
$523$	−1.43752e8	−	8.29951e7i	−1.00487	−	0.580160i	−0.0951815	−	0.995460i	$-0.530343\pi$
$523$	−1.43752e8	−	8.29951e7i	−1.00487	−	0.580160i	−0.909684	+	0.415300i	$0.863676\pi$
$524$			1.05087e8i			0.730394i
$525$		0			0
$526$	−2.37222e7			−0.163004
$527$	−1.49534e8	+	2.59000e8i	−1.02166	+	1.76957i
$528$	1.05634e7	−	6.09876e6i	0.0717629	−	0.0414324i
$529$	−5.03382e7	−	8.71883e7i	−0.340041	−	0.588967i
$530$	−5.17689e7	−	2.98888e7i	−0.347729	−	0.200761i
$531$			9.40956e7i			0.628472i
$532$		0			0
$533$	−2.65820e7			−0.175552
$534$	−7.38202e6	+	1.27860e7i	−0.0484788	+	0.0839677i
$535$	8.45064e7	−	4.87898e7i	0.551859	−	0.318616i
$536$	7.96839e7	+	1.38017e8i	0.517459	+	0.896266i
$537$	−1.06554e8	−	6.15188e7i	−0.688091	−	0.397269i
$538$			792991.i			0.00509238i
$539$		0			0
$540$	1.60438e7			0.101889
$541$	−6.31514e7	+	1.09381e8i	−0.398833	+	0.690799i	−0.993582	−	0.113112i	$-0.963918\pi$
$541$	−6.31514e7	+	1.09381e8i	−0.398833	+	0.690799i	0.594749	+	0.803911i	$0.297251\pi$
$542$	8.69464e7	−	5.01985e7i	0.546077	−	0.315278i
$543$	−2.05486e7	−	3.55912e7i	−0.128346	−	0.222302i
$544$	1.79312e8	+	1.03526e8i	1.11382	+	0.643062i
$545$			6.09727e7i			0.376657i
$546$		0			0
$547$	2.31931e8			1.41709			0.708545	−	0.705666i	$-0.249352\pi$
$547$	2.31931e8			1.41709			0.708545	+	0.705666i	$0.249352\pi$
$548$	8.23336e7	−	1.42606e8i	0.500306	−	0.866555i
$549$	2.47945e6	−	1.43151e6i	0.0149843	−	0.00865121i
$550$	−6.96468e6	−	1.20632e7i	−0.0418614	−	0.0725060i
$551$	−5.41729e7	−	3.12767e7i	−0.323838	−	0.186968i
$552$		−	1.01955e8i		−	0.606167i
$553$		0			0
$554$	2.07536e7			0.122057
$555$	6.57725e6	−	1.13921e7i	0.0384738	−	0.0666386i
$556$	1.79613e8	−	1.03700e8i	1.04499	−	0.603326i
$557$	−1.20538e8	−	2.08779e8i	−0.697525	−	1.20815i	−0.969322	−	0.245794i	$-0.920951\pi$
$557$	−1.20538e8	−	2.08779e8i	−0.697525	−	1.20815i	0.271797	−	0.962355i	$-0.412382\pi$
$558$	3.60867e7	+	2.08347e7i	0.207704	+	0.119918i
$559$		−	1.05308e8i		−	0.602872i
$560$		0			0
$561$	−4.33978e7			−0.245799
$562$	3.17071e7	−	5.49182e7i	0.178627	−	0.309391i
$563$	1.01477e8	−	5.85878e7i	0.568647	−	0.328308i	−0.187962	−	0.982176i	$-0.560188\pi$
$563$	1.01477e8	−	5.85878e7i	0.568647	−	0.328308i	0.756609	+	0.653868i	$0.226855\pi$
$564$	−1.99836e7	−	3.46126e7i	−0.111387	−	0.192929i
$565$	−1.47405e8	−	8.51042e7i	−0.817271	−	0.471852i
$566$			5.30821e7i			0.292751i
$567$		0			0
$568$	6.47488e7			0.353335
$569$	6.04302e7	−	1.04668e8i	0.328033	−	0.568170i	−0.654088	−	0.756418i	$-0.726948\pi$
$569$	6.04302e7	−	1.04668e8i	0.328033	−	0.568170i	0.982121	+	0.188248i	$0.0602809\pi$
$570$	1.08687e7	−	6.27503e6i	0.0586884	−	0.0338837i
$571$	−5.39062e7	−	9.33683e7i	−0.289555	−	0.501523i	0.684149	−	0.729342i	$-0.260174\pi$
$571$	−5.39062e7	−	9.33683e7i	−0.289555	−	0.501523i	−0.973703	+	0.227819i	$0.926841\pi$
$572$	−1.36138e7	−	7.85993e6i	−0.0727430	−	0.0419982i
$573$		−	1.92399e8i		−	1.02268i
$574$		0			0
$575$	1.37618e8			0.723887
$576$	677451.	−	1.17338e6i	0.00354495	−	0.00614004i
$577$	6.79444e7	−	3.92277e7i	0.353693	−	0.204205i	−0.312618	−	0.949879i	$-0.601206\pi$
$577$	6.79444e7	−	3.92277e7i	0.353693	−	0.204205i	0.666310	+	0.745674i	$0.267873\pi$
$578$	−2.78162e7	−	4.81791e7i	−0.144050	−	0.249503i
$579$	−1.80796e8	−	1.04382e8i	−0.931435	−	0.537764i
$580$			9.85778e7i			0.505237i
$581$		0			0
$582$	−3.23346e7			−0.164021
$583$	−4.41627e7	+	7.64920e7i	−0.222869	+	0.386020i
$584$	−1.34879e8	+	7.78724e7i	−0.677182	+	0.390971i
$585$	−7.02878e6	−	1.21742e7i	−0.0351085	−	0.0608097i
$586$	−1.09236e7	−	6.30674e6i	−0.0542841	−	0.0313410i
$587$			1.98030e8i			0.979075i	0.871982	+	0.489538i	$0.162834\pi$
$587$			1.98030e8i			0.979075i	−0.871982	+	0.489538i	$0.837166\pi$
$588$		0			0
$589$	−1.27789e8			−0.625387
$590$	5.79970e7	−	1.00454e8i	0.282390	−	0.489114i
$591$	1.27233e8	−	7.34581e7i	0.616365	−	0.355859i
$592$	8.98056e6	+	1.55548e7i	0.0432851	+	0.0749720i
$593$	3.26564e6	+	1.88542e6i	0.0156605	+	0.00904157i	0.507810	−	0.861469i	$-0.330455\pi$
$593$	3.26564e6	+	1.88542e6i	0.0156605	+	0.00904157i	−0.492149	+	0.870511i	$0.663789\pi$
$594$			6.04665e6i			0.0288506i
$595$		0			0
$596$	1.42512e8			0.673153
$597$	4.42475e7	−	7.66389e7i	0.207953	−	0.360186i
$598$	−3.43070e7	+	1.98071e7i	−0.160428	+	0.0926229i
$599$	−1.33653e8	−	2.31493e8i	−0.621867	−	1.07710i	−0.989138	−	0.146991i	$-0.953041\pi$
$599$	−1.33653e8	−	2.31493e8i	−0.621867	−	1.07710i	0.367271	−	0.930114i	$-0.380292\pi$
$600$	4.88560e7	+	2.82070e7i	0.226185	+	0.130588i
$601$			9.26866e7i			0.426966i	0.976947	+	0.213483i	$0.0684809\pi$
$601$			9.26866e7i			0.426966i	−0.976947	+	0.213483i	$0.931519\pi$
$602$		0			0
$603$	9.33790e7			0.425890
$604$	1.53770e7	−	2.66337e7i	0.0697846	−	0.120870i
$605$	−1.13339e8	+	6.54363e7i	−0.511815	+	0.295497i
$606$	−2.06010e7	−	3.56820e7i	−0.0925702	−	0.160336i
$607$	−1.38921e8	−	8.02061e7i	−0.621158	−	0.358625i	0.156162	−	0.987731i	$-0.450088\pi$
$607$	−1.38921e8	−	8.02061e7i	−0.621158	−	0.358625i	−0.777320	+	0.629106i	$0.783421\pi$
$608$			8.84718e7i			0.393635i
$609$		0			0
$610$	−3.52931e6			−0.0155489
$611$	−1.75096e7	+	3.03275e7i	−0.0767631	+	0.132958i
$612$	6.74985e7	−	3.89703e7i	0.294469	−	0.170012i
$613$	−3.60980e7	−	6.25236e7i	−0.156712	−	0.271433i	0.776969	−	0.629539i	$-0.216756\pi$
$613$	−3.60980e7	−	6.25236e7i	−0.156712	−	0.271433i	−0.933681	+	0.358106i	$0.883423\pi$
$614$	1.24837e8	+	7.20748e7i	0.539311	+	0.311371i
$615$			4.94151e7i			0.212439i
$616$		0			0
$617$	3.16720e6			0.0134841			0.00674203	−	0.999977i	$-0.497854\pi$
$617$	3.16720e6			0.0134841			0.00674203	+	0.999977i	$0.497854\pi$
$618$	2.94790e7	−	5.10592e7i	0.124896	−	0.216326i
$619$	−1.20117e8	+	6.93494e7i	−0.506444	+	0.292396i	−0.731371	−	0.681980i	$-0.761119\pi$
$619$	−1.20117e8	+	6.93494e7i	−0.506444	+	0.292396i	0.224927	+	0.974376i	$0.427786\pi$
$620$	1.00691e8	+	1.74403e8i	0.422491	+	0.731776i
$621$	−5.17355e7	−	2.98695e7i	−0.216030	−	0.124725i
$622$		−	1.20275e8i		−	0.499809i
$623$		0			0
$624$	1.91942e7			0.0789979
$625$	1.58233e7	−	2.74068e7i	0.0648124	−	0.112258i
$626$	−5.86869e7	+	3.38829e7i	−0.239231	+	0.138120i
$627$	−9.27178e6	−	1.60592e7i	−0.0376150	−	0.0651510i
$628$	6.31107e7	+	3.64370e7i	0.254814	+	0.147117i
$629$		−	6.39043e7i		−	0.256790i
$630$		0			0
$631$	−1.98716e8			−0.790944			−0.395472	−	0.918478i	$-0.629419\pi$
$631$	−1.98716e8			−0.790944			−0.395472	+	0.918478i	$0.629419\pi$
$632$	−6.88100e6	+	1.19182e7i	−0.0272584	+	0.0472129i
$633$	−1.42014e7	+	8.19920e6i	−0.0559914	+	0.0323266i
$634$	−3.67812e7	−	6.37069e7i	−0.144331	−	0.249988i
$635$	1.18462e8	+	6.83941e7i	0.462656	+	0.267114i
$636$		−	1.58628e8i		−	0.616608i
$637$		0			0
$638$	−3.71523e7			−0.143062
$639$	1.89693e7	−	3.28557e7i	0.0727022	−	0.125924i
$640$	1.50095e8	−	8.66573e7i	0.572567	−	0.330571i
$641$	−7.21736e7	−	1.25008e8i	−0.274034	−	0.474641i	0.695857	−	0.718180i	$-0.255025\pi$
$641$	−7.21736e7	−	1.25008e8i	−0.274034	−	0.474641i	−0.969891	+	0.243540i	$0.921691\pi$
$642$	−5.71995e7	−	3.30242e7i	−0.216166	−	0.124803i
$643$			2.68271e8i			1.00911i	0.863378	+	0.504557i	$0.168344\pi$
$643$			2.68271e8i			1.00911i	−0.863378	+	0.504557i	$0.831656\pi$
$644$		0			0
$645$	−1.95764e8			−0.729548
$646$	3.04840e7	−	5.27999e7i	0.113077	−	0.195855i
$647$	3.38971e8	−	1.95705e8i	1.25155	−	0.722585i	0.280136	−	0.959960i	$-0.409620\pi$
$647$	3.38971e8	−	1.95705e8i	1.25155	−	0.722585i	0.971418	+	0.237375i	$0.0762871\pi$
$648$	−1.22445e7	−	2.12081e7i	−0.0450003	−	0.0779428i
$649$	−1.48427e8	−	8.56944e7i	−0.542974	−	0.313486i
$650$		−	2.19194e7i		−	0.0798158i
$651$		0			0
$652$	2.84179e8			1.02529
$653$	−2.30591e8	+	3.99396e8i	−0.828139	+	1.43438i	0.0713566	+	0.997451i	$0.477267\pi$
$653$	−2.30591e8	+	3.99396e8i	−0.828139	+	1.43438i	−0.899496	+	0.436929i	$0.856066\pi$
$654$	3.57412e7	−	2.06352e7i	0.127772	−	0.0737692i
$655$	−8.55845e7	−	1.48237e8i	−0.304559	−	0.527512i
$656$	−5.84318e7	−	3.37356e7i	−0.206984	−	0.119503i
$657$			9.12561e7i			0.321785i
$658$		0			0
$659$	2.90612e8			1.01545			0.507724	−	0.861520i	$-0.330487\pi$
$659$	2.90612e8			1.01545			0.507724	+	0.861520i	$0.330487\pi$
$660$	−1.46114e7	+	2.53076e7i	−0.0508228	+	0.0880277i
$661$	2.43164e8	−	1.40391e8i	0.841965	−	0.486109i	−0.0159666	−	0.999873i	$-0.505083\pi$
$661$	2.43164e8	−	1.40391e8i	0.841965	−	0.486109i	0.857932	+	0.513764i	$0.171749\pi$
$662$	−3.85082e7	−	6.66981e7i	−0.132733	−	0.229900i
$663$	−5.91421e7	−	3.41457e7i	−0.202935	−	0.117164i
$664$		−	4.08496e8i		−	1.39535i
$665$		0			0
$666$	−8.90383e6			−0.0301408
$667$	1.83527e8	−	3.17878e8i	0.618475	−	1.07123i
$668$	−9.90926e7	+	5.72111e7i	−0.332439	+	0.191934i
$669$	7.76784e7	+	1.34543e8i	0.259431	+	0.449348i
$670$	−9.96886e7	−	5.75553e7i	−0.331452	−	0.191364i
$671$			5.21480e6i			0.0172611i
$672$		0			0
$673$	−2.35293e8			−0.771904			−0.385952	−	0.922519i	$-0.626127\pi$
$673$	−2.35293e8			−0.771904			−0.385952	+	0.922519i	$0.626127\pi$
$674$	−3.58530e7	+	6.20992e7i	−0.117097	+	0.202818i
$675$	2.86264e7	−	1.65274e7i	0.0930796	−	0.0537396i
$676$	1.10699e8	+	1.91736e8i	0.358346	+	0.620673i
$677$	5.35332e8	+	3.09074e8i	1.72527	+	0.996085i	0.906835	+	0.421486i	$0.138491\pi$
$677$	5.35332e8	+	3.09074e8i	1.72527	+	0.996085i	0.818435	+	0.574599i	$0.194842\pi$
$678$			1.15208e8i			0.369653i
$679$		0			0
$680$	−2.16665e8			−0.689069
$681$	1.43966e8	−	2.49357e8i	0.455848	−	0.789552i
$682$	−6.57295e7	+	3.79490e7i	−0.207208	+	0.119632i
$683$	−6.53722e6	−	1.13228e7i	−0.0205178	−	0.0355379i	0.855584	−	0.517664i	$-0.173198\pi$
$683$	−6.53722e6	−	1.13228e7i	−0.0205178	−	0.0355379i	−0.876102	+	0.482126i	$0.839865\pi$
$684$	2.88416e7	+	1.66517e7i	0.0901262	+	0.0520344i
$685$			2.68214e8i			0.834468i
$686$		0			0
$687$	2.12248e8			0.654595
$688$	1.33648e8	−	2.31485e8i	0.410390	−	0.710817i
$689$	−1.20369e8	+	6.94949e7i	−0.368007	+	0.212469i
$690$	3.68209e7	+	6.37756e7i	0.112085	+	0.194137i
$691$	−2.37346e8	−	1.37032e8i	−0.719362	−	0.415324i	0.0951555	−	0.995462i	$-0.469665\pi$
$691$	−2.37346e8	−	1.37032e8i	−0.719362	−	0.415324i	−0.814518	+	0.580138i	$0.802998\pi$
$692$			3.50855e8i			1.05879i
$693$		0			0
$694$	1.19878e8			0.358643
$695$	−1.68908e8	+	2.92558e8i	−0.503149	+	0.871480i
$696$	1.30308e8	−	7.52336e7i	0.386496	−	0.223143i
$697$	1.20029e8	+	2.07896e8i	0.354476	+	0.613971i
$698$	−8.05349e7	−	4.64968e7i	−0.236820	−	0.136728i
$699$		−	159096.i		−	0.000465831i
$700$		0			0
$701$	4.35624e8			1.26461			0.632307	−	0.774718i	$-0.282108\pi$
$701$	4.35624e8			1.26461			0.632307	+	0.774718i	$0.282108\pi$
$702$	−4.75754e6	+	8.24031e6i	−0.0137522	+	0.0238195i
$703$	2.36475e7	−	1.36529e7i	0.0680644	−	0.0392970i
$704$	1.23393e6	+	2.13723e6i	0.00353649	+	0.00612539i
$705$	5.63779e7	+	3.25498e7i	0.160895	+	0.0928925i
$706$		−	2.00740e8i		−	0.570454i
$707$		0			0
$708$	3.07807e8			0.867318
$709$	1.80906e8	−	3.13339e8i	0.507592	−	0.879176i	−0.492369	−	0.870387i	$-0.663869\pi$
$709$	1.80906e8	−	3.13339e8i	0.507592	−	0.879176i	0.999961	−	0.00878924i	$-0.00279774\pi$
$710$	−4.05020e7	+	2.33839e7i	−0.113162	+	0.0653343i
$711$	4.03181e6	+	6.98330e6i	0.0112174	+	0.0194291i
$712$	9.43202e7	+	5.44558e7i	0.261315	+	0.150870i
$713$		−	7.49848e8i		−	2.06873i
$714$		0			0
$715$	2.56049e7			0.0700495
$716$	−2.01241e8	+	3.48560e8i	−0.548249	+	0.949595i
$717$	−3.36916e7	+	1.94518e7i	−0.0914037	+	0.0527720i
$718$	−2.91663e7	−	5.05174e7i	−0.0787966	−	0.136480i
$719$	2.12503e8	+	1.22689e8i	0.571713	+	0.330079i	0.757833	−	0.652448i	$-0.226258\pi$
$719$	2.12503e8	+	1.22689e8i	0.571713	+	0.330079i	−0.186120	+	0.982527i	$0.559591\pi$
$720$		−	3.56814e7i		−	0.0955969i
$721$		0			0
$722$	−1.43620e8			−0.381595
$723$	−4.26377e7	+	7.38506e7i	−0.112818	+	0.195407i
$724$	−1.16426e8	+	6.72188e7i	−0.306786	+	0.177123i
$725$	1.01549e8	+	1.75888e8i	0.266479	+	0.461555i
$726$	7.67153e7	+	4.42916e7i	0.200480	+	0.115747i
$727$			2.59949e8i			0.676526i	0.941052	+	0.338263i	$0.109839\pi$
$727$			2.59949e8i			0.676526i	−0.941052	+	0.338263i	$0.890161\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$	5.62468e7	−	9.74223e7i	0.144587	−	0.250432i
$731$	−8.23606e8	+	4.75509e8i	−2.10847	+	1.21733i
$732$	−4.68277e6	−	8.11080e6i	−0.0119390	−	0.0206790i
$733$	1.08280e8	+	6.25152e7i	0.274938	+	0.158735i	0.631129	−	0.775678i	$-0.282592\pi$
$733$	1.08280e8	+	6.25152e7i	0.274938	+	0.158735i	−0.356192	+	0.934413i	$0.615925\pi$
$734$			4.04915e7i			0.102394i
$735$		0			0
$736$	−5.19138e8			−1.30212
$737$	−8.50418e7	+	1.47297e8i	−0.212437	+	0.367951i
$738$	2.89663e7	−	1.67237e7i	0.0720649	−	0.0416067i
$739$	2.82361e8	+	4.89063e8i	0.699634	+	1.21180i	0.968593	+	0.248650i	$0.0799869\pi$
$739$	2.82361e8	+	4.89063e8i	0.699634	+	1.21180i	−0.268960	+	0.963151i	$0.586680\pi$
$740$	−3.72661e7	−	2.15156e7i	−0.0919641	−	0.0530955i
$741$		−	2.91804e7i		−	0.0717194i
$742$		0			0
$743$	2.68677e8			0.655035			0.327518	−	0.944845i	$-0.393788\pi$
$743$	2.68677e8			0.655035			0.327518	+	0.944845i	$0.393788\pi$
$744$	1.53694e8	−	2.66205e8i	0.373196	−	0.646394i
$745$	−2.01029e8	+	1.16064e8i	−0.486171	+	0.280691i
$746$	7.21256e7	+	1.24925e8i	0.173729	+	0.300908i
$747$	−2.07284e8	−	1.19676e8i	−0.497285	−	0.287107i
$748$			1.41964e8i			0.339213i
$749$		0			0
$750$	−1.13709e8			−0.269533
$751$	−1.95480e8	+	3.38581e8i	−0.461512	+	0.799362i	−0.999037	−	0.0438862i	$-0.986026\pi$
$751$	−1.95480e8	+	3.38581e8i	−0.461512	+	0.799362i	0.537525	+	0.843248i	$0.319359\pi$
$752$	−7.69783e7	+	4.44434e7i	−0.181015	+	0.104509i
$753$	−1.70245e7	−	2.94873e7i	−0.0398740	−	0.0690637i
$754$	−5.06308e7	−	2.92317e7i	−0.118114	−	0.0681930i
$755$			5.00927e7i			0.116395i
$756$		0			0
$757$	−5.67872e8			−1.30907			−0.654535	−	0.756031i	$-0.727136\pi$
$757$	−5.67872e8			−1.30907			−0.654535	+	0.756031i	$0.727136\pi$
$758$	5.26726e7	−	9.12317e7i	0.120942	−	0.209478i
$759$	9.42327e7	−	5.44053e7i	0.215515	−	0.124427i
$760$	−4.62897e7	−	8.01762e7i	−0.105449	−	0.182644i
$761$	1.66316e8	+	9.60225e7i	0.377381	+	0.217881i	0.676678	−	0.736279i	$-0.263419\pi$
$761$	1.66316e8	+	9.60225e7i	0.377381	+	0.217881i	−0.299297	+	0.954160i	$0.596752\pi$
$762$		−	9.25873e7i		−	0.209260i
$763$		0			0
$764$	−6.29378e8			−1.41134
$765$	−6.34758e7	+	1.09943e8i	−0.141783	+	0.245575i
$766$	−1.43243e8	+	8.27015e7i	−0.318704	+	0.184004i
$767$	−1.34850e8	−	2.33567e8i	−0.298858	−	0.517637i
$768$	−1.06412e8	−	6.14368e7i	−0.234912	−	0.135627i
$769$		−	7.75766e8i		−	1.70589i	−0.521999	−	0.852946i	$-0.674813\pi$
$769$		−	7.75766e8i		−	1.70589i	0.521999	−	0.852946i	$-0.325187\pi$
$770$		0			0
$771$	−4.90748e8			−1.07077
$772$	−3.41457e8	+	5.91421e8i	−0.742138	+	1.28542i
$773$	−2.34180e7	+	1.35204e7i	−0.0507005	+	0.0292719i	−0.525136	−	0.851018i	$-0.675986\pi$
$773$	−2.34180e7	+	1.35204e7i	−0.0507005	+	0.0292719i	0.474436	+	0.880290i	$0.342652\pi$
$774$	6.62530e7	+	1.14754e8i	0.142884	+	0.247482i
$775$	3.59320e8	+	2.07453e8i	0.771926	+	0.445672i
$776$			2.38527e8i			0.510448i
$777$		0			0
$778$	−5.57154e7			−0.118314
$779$	−5.12874e7	+	8.88323e7i	−0.108492	+	0.187914i
$780$	−3.98244e7	+	2.29926e7i	−0.0839200	+	0.0484512i
$781$	3.45512e7	+	5.98445e7i	0.0725288	+	0.125624i
$782$	3.09821e8	+	1.78875e8i	0.647874	+	0.374050i
$783$		−	8.81638e7i		−	0.183656i
$784$		0			0
$785$	−1.18699e8			−0.245379
$786$	−5.79293e7	+	1.00336e8i	−0.119297	+	0.206629i
$787$	3.68573e8	−	2.12796e8i	0.756136	−	0.436555i	−0.0717707	−	0.997421i	$-0.522865\pi$
$787$	3.68573e8	−	2.12796e8i	0.756136	−	0.436555i	0.827907	+	0.560866i	$0.189532\pi$
$788$	−2.40297e8	−	4.16207e8i	−0.491100	−	0.850610i
$789$	8.87979e7	+	5.12675e7i	0.180789	+	0.104379i
$790$		−	9.94022e6i		−	0.0201611i
$791$		0			0
$792$	4.46050e7			0.0897859
$793$	−4.10303e6	+	7.10666e6i	−0.00822783	+	0.0142510i
$794$	−9.18709e7	+	5.30417e7i	−0.183534	+	0.105963i
$795$	1.29189e8	+	2.23762e8i	0.257113	+	0.445333i
$796$	−2.50702e8	−	1.44743e8i	−0.497072	−	0.286985i
$797$			7.51386e7i			0.148419i	0.997243	+	0.0742093i	$0.0236433\pi$
$797$			7.51386e7i			0.148419i	−0.997243	+	0.0742093i	$0.976357\pi$
$798$		0			0
$799$	3.16253e8			0.620003
$800$	1.43625e8	−	2.48766e8i	0.280518	−	0.485871i
$801$	5.52654e7	−	3.19075e7i	0.107536	−	0.0620862i
$802$	−2.05590e8	−	3.56093e8i	−0.398547	−	0.690304i
$803$	−1.43948e8	−	8.31084e7i	−0.278009	−	0.160509i
$804$		−	3.05462e8i		−	0.587746i
$805$		0			0
$806$	−1.19434e8			−0.228099
$807$	1.71378e6	−	2.96835e6i	0.00326088	−	0.00564801i
$808$	−2.63220e8	+	1.51970e8i	−0.498981	+	0.288087i
$809$	3.91158e8	+	6.77506e8i	0.738766	+	1.27958i	0.953051	+	0.302810i	$0.0979246\pi$
$809$	3.91158e8	+	6.77506e8i	0.738766	+	1.27958i	−0.214285	+	0.976771i	$0.568742\pi$
$810$	1.53185e7	+	8.84412e6i	0.0288244	+	0.0166418i
$811$			8.00635e8i			1.50097i	0.660888	+	0.750485i	$0.270180\pi$
$811$			8.00635e8i			1.50097i	−0.660888	+	0.750485i	$0.729820\pi$
$812$		0			0
$813$	−4.33948e8			−0.807544
$814$	8.10887e6	−	1.40450e7i	0.0150344	−	0.0260404i
$815$	−4.00863e8	+	2.31439e8i	−0.740497	+	0.427526i
$816$	−8.66697e7	−	1.50116e8i	−0.159513	−	0.276285i
$817$	−3.51921e8	−	2.03181e8i	−0.645325	−	0.372579i
$818$			1.24637e8i			0.227712i
$819$		0			0
$820$	1.61647e8			0.293175
$821$	1.37831e8	−	2.38730e8i	0.249067	−	0.431397i	−0.714200	−	0.699942i	$-0.753209\pi$
$821$	1.37831e8	−	2.38730e8i	0.249067	−	0.431397i	0.963267	+	0.268544i	$0.0865426\pi$
$822$	1.57223e8	−	9.07725e7i	0.283074	−	0.163433i
$823$	3.78952e8	+	6.56364e8i	0.679806	+	1.17746i	0.975039	+	0.222033i	$0.0712693\pi$
$823$	3.78952e8	+	6.56364e8i	0.679806	+	1.17746i	−0.295233	+	0.955425i	$0.595397\pi$
$824$	−3.76654e8	−	2.17461e8i	−0.673226	−	0.388687i
$825$			6.02072e7i			0.107223i
$826$		0			0
$827$	3.06595e8			0.542061			0.271030	−	0.962571i	$-0.412636\pi$
$827$	3.06595e8			0.542061			0.271030	+	0.962571i	$0.412636\pi$
$828$	−9.77095e7	+	1.69238e8i	−0.172126	+	0.298130i
$829$	−1.07092e8	+	6.18296e7i	−0.187972	+	0.108526i	−0.591033	−	0.806647i	$-0.701280\pi$
$829$	−1.07092e8	+	6.18296e7i	−0.187972	+	0.108526i	0.403061	+	0.915173i	$0.367946\pi$
$830$	1.47527e8	+	2.55525e8i	0.258011	+	0.446888i
$831$	−7.76858e7	−	4.48519e7i	−0.135375	−	0.0781588i
$832$			3.88346e6i			0.00674293i
$833$		0			0
$834$	2.28657e8			0.394172
$835$	9.31869e7	−	1.61405e8i	0.160065	−	0.277240i
$836$	−5.25330e7	+	3.03300e7i	−0.0899112	+	0.0519102i
$837$	−9.00542e7	−	1.55978e8i	−0.153577	−	0.266004i
$838$	−1.16781e8	−	6.74238e7i	−0.198446	−	0.114573i
$839$			2.04720e8i			0.346637i	0.984866	+	0.173318i	$0.0554489\pi$
$839$			2.04720e8i			0.346637i	−0.984866	+	0.173318i	$0.944551\pi$
$840$		0			0
$841$	−5.31198e7			−0.0893035
$842$	−1.07097e8	+	1.85497e8i	−0.179407	+	0.310743i
$843$	−2.37374e8	+	1.37048e8i	−0.396233	+	0.228765i
$844$	2.68213e7	+	4.64559e7i	0.0446121	+	0.0772705i
$845$	−3.12304e8	−	1.80309e8i	−0.517615	−	0.298845i
$846$		−	4.40637e7i		−	0.0727729i
$847$		0			0
$848$	−3.52789e8			−0.578532
$849$	1.14719e8	−	1.98699e8i	0.187462	−	0.324693i
$850$	−1.71430e8	+	9.89754e7i	−0.279146	+	0.161165i
$851$	8.01131e7	+	1.38760e8i	0.129991	+	0.225152i
$852$	−1.07478e8	−	6.20525e7i	−0.173780	−	0.100332i
$853$		−	1.81851e8i		−	0.293001i	−0.989211	−	0.146500i	$-0.953199\pi$
$853$		−	1.81851e8i		−	0.293001i	0.989211	−	0.146500i	$-0.0468010\pi$
$854$		0			0
$855$	−5.42454e7			−0.0867890
$856$	−2.43613e8	+	4.21950e8i	−0.388400	+	0.672729i
$857$	5.32176e8	−	3.07252e8i	0.845499	−	0.488149i	−0.0136307	−	0.999907i	$-0.504339\pi$
$857$	5.32176e8	−	3.07252e8i	0.845499	−	0.488149i	0.859130	+	0.511758i	$0.171006\pi$
$858$	−8.66554e6	−	1.50092e7i	−0.0137194	−	0.0237626i
$859$	1.89532e8	+	1.09426e8i	0.299022	+	0.172640i	0.642003	−	0.766702i	$-0.278103\pi$
$859$	1.89532e8	+	1.09426e8i	0.299022	+	0.172640i	−0.342981	+	0.939342i	$0.611437\pi$
$860$			6.40386e8i			1.00681i
$861$		0			0
$862$	2.14729e8			0.335250
$863$	3.29715e8	−	5.71084e8i	0.512988	−	0.888521i	−0.486899	−	0.873458i	$-0.661872\pi$
$863$	3.29715e8	−	5.71084e8i	0.512988	−	0.888521i	0.999887	−	0.0150623i	$-0.00479467\pi$
$864$	−1.07988e8	+	6.23467e7i	−0.167430	+	0.0966657i
$865$	−2.85741e8	−	4.94918e8i	−0.441494	−	0.764689i
$866$	−2.00121e8	−	1.15540e8i	−0.308133	−	0.177901i
$867$			2.40461e8i			0.368967i
$868$		0			0
$869$	−1.46873e7			−0.0223812
$870$	−5.43408e7	+	9.41211e7i	−0.0825218	+	0.142932i
$871$	−2.31788e8	+	1.33823e8i	−0.350781	+	0.202524i
$872$	−1.52222e8	−	2.63656e8i	−0.229577	−	0.397639i
$873$	1.21036e8	+	6.98804e7i	0.181917	+	0.105030i
$874$			1.52864e8i			0.228966i
$875$		0			0
$876$	2.98518e8			0.444077
$877$	−8.11828e7	+	1.40613e8i	−0.120355	+	0.208462i	−0.919908	−	0.392135i	$-0.871737\pi$
$877$	−8.11828e7	+	1.40613e8i	−0.120355	+	0.208462i	0.799552	+	0.600596i	$0.205070\pi$
$878$	4.75256e8	−	2.74389e8i	0.702173	−	0.405400i
$879$	2.72598e7	+	4.72153e7i	0.0401380	+	0.0695210i
$880$	5.62840e7	+	3.24956e7i	0.0825918	+	0.0476844i
$881$		−	8.48365e8i		−	1.24067i	−0.784338	−	0.620333i	$-0.786997\pi$
$881$		−	8.48365e8i		−	1.24067i	0.784338	−	0.620333i	$-0.213003\pi$
$882$		0			0
$883$	3.14592e8			0.456947			0.228473	−	0.973550i	$-0.426627\pi$
$883$	3.14592e8			0.456947			0.228473	+	0.973550i	$0.426627\pi$
$884$	−1.11698e8	+	1.93466e8i	−0.161692	+	0.280058i
$885$	−4.34193e8	+	2.50682e8i	−0.626402	+	0.361654i
$886$	6.23635e7	+	1.08017e8i	0.0896663	+	0.155307i
$887$	7.25058e8	+	4.18612e8i	1.03897	+	0.599848i	0.919540	−	0.392995i	$-0.128561\pi$
$887$	7.25058e8	+	4.18612e8i	1.03897	+	0.599848i	0.119426	+	0.992843i	$0.461894\pi$
$888$			6.56819e7i			0.0938009i
$889$		0			0
$890$	−7.86663e7			−0.111588
$891$	1.30678e7	−	2.26341e7i	0.0184743	−	0.0319985i
$892$	4.40119e8	−	2.54103e8i	0.620119	−	0.358026i
$893$	6.75662e7	+	1.17028e8i	0.0948800	+	0.164337i
$894$	1.36069e8	+	7.85597e7i	0.190436	+	0.109948i
$895$		−	6.55573e8i		−	0.914433i
$896$		0			0
$897$	1.71226e8			0.237242
$898$	−2.41267e8	+	4.17886e8i	−0.333172	+	0.577070i
$899$	9.58376e8	−	5.53319e8i	1.31904	−	0.761546i
$900$	−5.40647e7	−	9.36429e7i	−0.0741629	−	0.128454i
$901$	1.08703e9	+	6.27598e8i	1.48617	+	0.858039i
$902$			6.09222e7i			0.0830148i
$903$		0			0
$904$	8.49870e8			1.15040
$905$	1.09488e8	−	1.89638e8i	0.147713	−	0.255847i
$906$	2.93635e7	−	1.69530e7i	0.0394842	−	0.0227962i
$907$	−3.44024e8	−	5.95867e8i	−0.461070	−	0.798596i	0.537945	−	0.842980i	$-0.319201\pi$
$907$	−3.44024e8	−	5.95867e8i	−0.461070	−	0.798596i	−0.999015	+	0.0443839i	$0.985868\pi$
$908$	−8.15700e8	−	4.70945e8i	−1.08962	−	0.629090i
$909$			1.78089e8i			0.237107i
$910$		0			0
$911$	2.31613e8			0.306343			0.153171	−	0.988200i	$-0.451051\pi$
$911$	2.31613e8			0.306343			0.153171	+	0.988200i	$0.451051\pi$
$912$	3.70333e7	−	6.41436e7i	0.0488211	−	0.0845607i
$913$	3.77555e8	−	2.17981e8i	0.496098	−	0.286422i
$914$	2.75045e7	+	4.76393e7i	0.0360218	+	0.0623917i
$915$	1.32111e7	+	7.62741e6i	0.0172455	+	0.00995667i
$916$		−	6.94307e8i		−	0.903369i
$917$		0			0
$918$	8.59292e7			0.111074
$919$	5.62582e8	−	9.74420e8i	0.724835	−	1.25545i	−0.234207	−	0.972187i	$-0.575249\pi$
$919$	5.62582e8	−	9.74420e8i	0.724835	−	1.25545i	0.959042	−	0.283264i	$-0.0914174\pi$
$920$	4.70461e8	−	2.71621e8i	0.604171	−	0.348818i
$921$	−3.11530e8	−	5.39587e8i	−0.398769	−	0.690689i
$922$	−9.52653e7	−	5.50014e7i	−0.121546	−	0.0701748i
$923$			1.08740e8i			0.138289i
$924$		0			0
$925$	−8.86565e7			−0.112017
$926$	−2.91515e8	+	5.04918e8i	−0.367136	+	0.635899i
$927$	−2.20694e8	+	1.27418e8i	−0.277046	+	0.159953i
$928$	−3.83076e8	−	6.63507e8i	−0.479337	−	0.830237i
$929$	5.93421e8	+	3.42612e8i	0.740143	+	0.427322i	0.822121	−	0.569312i	$-0.192790\pi$
$929$	5.93421e8	+	3.42612e8i	0.740143	+	0.427322i	−0.0819782	+	0.996634i	$0.526124\pi$
$930$			2.22024e8i			0.276027i
$931$		0			0
$932$	−520438.			−0.000642867
$933$	−2.59933e8	+	4.50218e8i	−0.320049	+	0.554342i
$934$	−2.05871e8	+	1.18860e8i	−0.252670	+	0.145879i
$935$	−1.15617e8	−	2.00254e8i	−0.141445	−	0.244989i
$936$	6.07872e7	+	3.50955e7i	0.0741284	+	0.0427980i
$937$			7.87984e8i			0.957852i	0.877855	+	0.478926i	$0.158974\pi$
$937$			7.87984e8i			0.957852i	−0.877855	+	0.478926i	$0.841026\pi$
$938$		0			0
$939$	2.92905e8			0.353778
$940$	1.06477e8	−	1.84424e8i	0.128196	−	0.222041i
$941$	−1.79551e8	+	1.03664e8i	−0.215486	+	0.124411i	−0.603859	−	0.797092i	$-0.706371\pi$
$941$	−1.79551e8	+	1.03664e8i	−0.215486	+	0.124411i	0.388372	+	0.921503i	$0.373037\pi$
$942$	4.01716e7	+	6.95793e7i	0.0480581	+	0.0832391i
$943$	−5.21254e8	−	3.00946e8i	−0.621604	−	0.358883i
$944$		−	6.84561e8i		−	0.813759i
$945$		0			0
$946$	−2.41351e8			−0.285086
$947$	1.77030e8	−	3.06624e8i	0.208447	−	0.361041i	−0.742778	−	0.669537i	$-0.766492\pi$
$947$	1.77030e8	−	3.06624e8i	0.208447	−	0.361041i	0.951226	+	0.308496i	$0.0998258\pi$
$948$	2.28439e7	−	1.31889e7i	0.0268129	−	0.0154805i
$949$	−1.30780e8	−	2.26518e8i	−0.153019	−	0.265036i
$950$	−7.32509e7	−	4.22914e7i	−0.0854363	−	0.0493267i
$951$			3.17960e8i			0.369685i
$952$		0			0
$953$	−4.28652e8			−0.495252			−0.247626	−	0.968856i	$-0.579650\pi$
$953$	−4.28652e8			−0.495252			−0.247626	+	0.968856i	$0.579650\pi$
$954$	8.74436e7	−	1.51457e8i	0.100712	−	0.174439i
$955$	8.87803e8	−	5.12573e8i	1.01931	−	0.588499i
$956$	6.36311e7	+	1.10212e8i	0.0728276	+	0.126141i
$957$	1.39070e8	+	8.02922e7i	0.158671	+	0.0916089i
$958$		−	3.31711e8i		−	0.377280i
$959$		0			0
$960$	7.21923e6			0.00815975
$961$	6.86614e8	−	1.18925e9i	0.773646	−	1.33999i
$962$	2.21013e7	−	1.27602e7i	0.0248252	−	0.0143329i
$963$	1.42741e8	+	2.47235e8i	0.159834	+	0.276841i
$964$	2.41581e8	+	1.39477e8i	0.269669	+	0.155694i
$965$		−	1.11235e9i		−	1.23782i
$966$		0			0
$967$	1.16972e9			1.29361			0.646805	−	0.762655i	$-0.276105\pi$
$967$	1.16972e9			1.29361			0.646805	+	0.762655i	$0.276105\pi$
$968$	3.26731e8	−	5.65915e8i	0.360217	−	0.623914i
$969$	−2.28218e8	+	1.31762e8i	−0.250829	+	0.144816i
$970$	−8.61432e7	−	1.49204e8i	−0.0943856	−	0.163481i
$971$	−6.09512e8	−	3.51902e8i	−0.665770	−	0.384383i	0.128702	−	0.991683i	$-0.458919\pi$
$971$	−6.09512e8	−	3.51902e8i	−0.665770	−	0.384383i	−0.794472	+	0.607301i	$0.792252\pi$
$972$			4.69383e7i			0.0511127i
$973$		0			0
$974$	6.87949e8			0.744525
$975$	−4.73714e7	+	8.20497e7i	−0.0511096	+	0.0885244i
$976$	−1.80384e7	+	1.04145e7i	−0.0194021	+	0.0112018i
$977$	−2.21206e8	−	3.83140e8i	−0.237199	−	0.410841i	0.722710	−	0.691151i	$-0.242896\pi$
$977$	−2.21206e8	−	3.83140e8i	−0.237199	−	0.410841i	−0.959910	+	0.280310i	$0.909563\pi$
$978$	2.71331e8	+	1.56653e8i	0.290056	+	0.167464i
$979$			1.16235e8i			0.123876i
$980$		0			0
$981$	−1.78384e8			−0.188951
$982$	1.59679e8	−	2.76571e8i	0.168621	−	0.292061i
$983$	1.01182e9	−	5.84175e8i	1.06523	−	0.615011i	0.138355	−	0.990383i	$-0.455818\pi$
$983$	1.01182e9	−	5.84175e8i	1.06523	−	0.615011i	0.926874	+	0.375372i	$0.122485\pi$
$984$	−1.23368e8	−	2.13679e8i	−0.129484	−	0.224273i
$985$	6.77928e8	+	3.91402e8i	0.709374	+	0.409557i
$986$			5.27974e8i			0.550784i
$987$		0			0
$988$	−9.54552e7			−0.0989758
$989$	1.19224e9	−	2.06501e9i	1.23246	−	2.13468i
$990$	−2.79016e7	+	1.61090e7i	−0.0287556	+	0.0166021i
$991$	5.01818e8	+	8.69174e8i	0.515615	+	0.893071i	0.999836	+	0.0181249i	$0.00576967\pi$
$991$	5.01818e8	+	8.69174e8i	0.515615	+	0.893071i	−0.484221	+	0.874946i	$0.660897\pi$
$992$	−1.35547e9	−	7.82580e8i	−1.38853	−	0.801666i
$993$			3.32890e8i			0.339979i
$994$		0			0
$995$	4.71522e8			0.478666
$996$	−3.91485e8	+	6.78072e8i	−0.396220	+	0.686274i
$997$	−1.60115e9	+	9.24424e8i	−1.61565	+	0.932794i	−0.627619	+	0.778521i	$0.715970\pi$
$997$	−1.60115e9	+	9.24424e8i	−1.61565	+	0.932794i	−0.988028	+	0.154274i	$0.950696\pi$
$998$	−9.44016e7	−	1.63508e8i	−0.0949703	−	0.164493i
$999$	3.33292e7	+	1.92426e7i	0.0334294	+	0.0193005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.7.f.a.19.3		8
7.2	even	3		147.7.d.a.97.3		8
7.3	odd	6	inner	147.7.f.a.31.3		8
7.4	even	3		21.7.f.b.10.3	✓	8
7.5	odd	6		147.7.d.a.97.4		8
7.6	odd	2		21.7.f.b.19.3	yes	8
21.2	odd	6		441.7.d.d.244.5		8
21.5	even	6		441.7.d.d.244.6		8
21.11	odd	6		63.7.m.c.10.2		8
21.20	even	2		63.7.m.c.19.2		8
28.11	odd	6		336.7.bh.b.241.3		8
28.27	even	2		336.7.bh.b.145.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.3	✓	8	7.4	even	3
21.7.f.b.19.3	yes	8	7.6	odd	2
63.7.m.c.10.2		8	21.11	odd	6
63.7.m.c.19.2		8	21.20	even	2
147.7.d.a.97.3		8	7.2	even	3
147.7.d.a.97.4		8	7.5	odd	6
147.7.f.a.19.3		8	1.1	even	1	trivial
147.7.f.a.31.3		8	7.3	odd	6	inner
336.7.bh.b.145.3		8	28.27	even	2
336.7.bh.b.241.3		8	28.11	odd	6
441.7.d.d.244.5		8	21.2	odd	6
441.7.d.d.244.6		8	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	147.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.80325 - 3.12332i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(25.4966 + 44.1614i) q^{4} +(-71.9311 - 41.5295i) q^{5} +56.2198i q^{6} +414.723 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(1.80325 - 3.12332i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(25.4966 + 44.1614i) q^{4} +(-71.9311 - 41.5295i) q^{5} +56.2198i q^{6} +414.723 q^{8} +(121.500 - 210.444i) q^{9} +(-259.420 + 149.776i) q^{10} +(221.304 + 383.310i) q^{11} +(-688.408 - 397.452i) q^{12} +696.494i q^{13} +1294.76 q^{15} +(-883.932 + 1531.01i) q^{16} +(5447.24 - 3144.96i) q^{17} +(-438.190 - 758.967i) q^{18} +(2327.56 + 1343.82i) q^{19} -4235.44i q^{20} +1596.27 q^{22} +(-7885.31 + 13657.8i) q^{23} +(-5598.76 + 3232.44i) q^{24} +(-4363.11 - 7557.12i) q^{25} +(2175.37 + 1255.95i) q^{26} +3788.00i q^{27} -23274.5 q^{29} +(2334.78 - 4043.95i) q^{30} +(-41177.0 + 23773.6i) q^{31} +(16459.0 + 28507.9i) q^{32} +(-5975.21 - 3449.79i) q^{33} -22684.6i q^{34} +12391.3 q^{36} +(5079.89 - 8798.64i) q^{37} +(8394.35 - 4846.48i) q^{38} +(-5428.63 - 9402.67i) q^{39} +(-29831.5 - 17223.2i) q^{40} +38165.4i q^{41} -151197. q^{43} +(-11285.0 + 19546.2i) q^{44} +(-17479.3 + 10091.7i) q^{45} +(28438.4 + 49256.7i) q^{46} +(43543.1 + 25139.6i) q^{47} -27558.3i q^{48} -31471.1 q^{50} +(-49025.1 + 84914.0i) q^{51} +(-30758.1 + 17758.2i) q^{52} +(99778.2 + 172821. i) q^{53} +(11831.1 + 6830.70i) q^{54} -36762.6i q^{55} -41896.1 q^{57} +(-41969.8 + 72693.8i) q^{58} +(-335347. + 193612. i) q^{59} +(33012.0 + 57178.4i) q^{60} +(10203.5 + 5890.98i) q^{61} +171479. i q^{62} +5575.73 q^{64} +(28925.0 - 50099.6i) q^{65} +(-21549.6 + 12441.7i) q^{66} +(192138. + 332792. i) q^{67} +(277772. + 160372. i) q^{68} -245840. i q^{69} +156126. q^{71} +(50388.8 - 87276.0i) q^{72} +(-325227. + 187770. i) q^{73} +(-18320.6 - 31732.3i) q^{74} +(117804. + 68014.1i) q^{75} +137051. i q^{76} -39156.7 q^{78} +(-16591.8 + 28737.9i) q^{79} +(127164. - 73418.4i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(119203. + 68821.8i) q^{82} -984986. i q^{83} -522434. q^{85} +(-272646. + 472237. i) q^{86} +(314206. - 181407. i) q^{87} +(91779.9 + 158967. i) q^{88} +(227430. + 131307. i) q^{89} +72791.1i q^{90} -804193. q^{92} +(370593. - 641886. i) q^{93} +(157038. - 90666.0i) q^{94} +(-111616. - 193325. i) q^{95} +(-444394. - 256571. i) q^{96} +575147. i q^{97} +107554. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} + 42 q^{5} - 454 q^{8} + 972 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 + 42 * q^5 - 454 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} + 42 q^{5} - 454 q^{8} + 972 q^{9} - 261 q^{10} - 1070 q^{11} + 4671 q^{12} - 756 q^{15} + 3911 q^{16} - 7212 q^{17} + 1215 q^{18} + 24606 q^{19} - 78 q^{22} - 15224 q^{23} + 6129 q^{24} + 22274 q^{25} + 19044 q^{26} + 32524 q^{29} + 2349 q^{30} - 40200 q^{31} + 70203 q^{32} + 28890 q^{33} - 84078 q^{36} - 45670 q^{37} - 503310 q^{38} + 93366 q^{39} + 94941 q^{40} - 445660 q^{43} - 188829 q^{44} + 10206 q^{45} + 525804 q^{46} - 82884 q^{47} - 1218884 q^{50} + 64908 q^{51} - 722856 q^{52} - 13034 q^{53} - 32805 q^{54} - 442908 q^{57} - 159501 q^{58} - 1810362 q^{59} + 429705 q^{60} + 392856 q^{61} - 1410446 q^{64} - 389004 q^{65} + 1053 q^{66} + 384094 q^{67} + 1616346 q^{68} + 225688 q^{71} - 55161 q^{72} - 903078 q^{73} + 1185530 q^{74} - 601398 q^{75} - 342792 q^{78} - 559592 q^{79} - 847713 q^{80} - 236196 q^{81} - 347634 q^{82} + 1953576 q^{85} - 2302402 q^{86} - 439074 q^{87} + 304887 q^{88} + 1770036 q^{89} - 113064 q^{92} + 361800 q^{93} + 1837620 q^{94} + 1160112 q^{95} - 1895481 q^{96} - 520020 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 + 42 * q^5 - 454 * q^8 + 972 * q^9 - 261 * q^10 - 1070 * q^11 + 4671 * q^12 - 756 * q^15 + 3911 * q^16 - 7212 * q^17 + 1215 * q^18 + 24606 * q^19 - 78 * q^22 - 15224 * q^23 + 6129 * q^24 + 22274 * q^25 + 19044 * q^26 + 32524 * q^29 + 2349 * q^30 - 40200 * q^31 + 70203 * q^32 + 28890 * q^33 - 84078 * q^36 - 45670 * q^37 - 503310 * q^38 + 93366 * q^39 + 94941 * q^40 - 445660 * q^43 - 188829 * q^44 + 10206 * q^45 + 525804 * q^46 - 82884 * q^47 - 1218884 * q^50 + 64908 * q^51 - 722856 * q^52 - 13034 * q^53 - 32805 * q^54 - 442908 * q^57 - 159501 * q^58 - 1810362 * q^59 + 429705 * q^60 + 392856 * q^61 - 1410446 * q^64 - 389004 * q^65 + 1053 * q^66 + 384094 * q^67 + 1616346 * q^68 + 225688 * q^71 - 55161 * q^72 - 903078 * q^73 + 1185530 * q^74 - 601398 * q^75 - 342792 * q^78 - 559592 * q^79 - 847713 * q^80 - 236196 * q^81 - 347634 * q^82 + 1953576 * q^85 - 2302402 * q^86 - 439074 * q^87 + 304887 * q^88 + 1770036 * q^89 - 113064 * q^92 + 361800 * q^93 + 1837620 * q^94 + 1160112 * q^95 - 1895481 * q^96 - 520020 * q^99

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